generator string | id string | conversations list | source string | thinking int64 |
|---|---|---|---|---|
DeepSeek-R1-0528 | cda83850-fbb6-447c-97fb-59c111a5596a | [
{
"content": "Evaluate the definite integral $\\int_0^1(1-\\sqrt[2024]x)^{2024}\\,dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe definite integral to evaluate is \\(\\int_0^1 (1 - \\sqrt[2024]{x})^{2024} dx\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 80eba578-3c17-4152-9bc5-5ab80236fbcc | [
{
"content": "Determine the quadrant in which the point $(\\cos{B}-\\sin{A}, \\sin{B}-\\cos{A})$ lies, given that $\\triangle{ABC}$ is a triangle with three acute angles A, B, and C.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 481b8bf4-3e6a-4976-b2e8-f35f0c0b0e4a | [
{
"content": "Zoey read 15 books, one at a time. The first book took her 1 day to read, the second book took her 2 days to read, the third book took her 3 days to read, and so on, with each book taking her 1 more day to read than the previous book. Zoey finished the first book on a Monday, and the second on a W... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 2961b3c3-1414-4615-b02d-d3592c1c7cb6 | [
{
"content": "Let \\( A \\) be the set of the 16 first positive integers. Find the least positive integer \\( k \\) such that in every \\( k \\)-subset of \\( A \\), there exist two distinct elements \\( a, b \\in A \\) such that \\( a^2 + b^2 \\) is a prime number.\nPlease reason step by step, and put your fin... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 6f94e3aa-9fae-42cd-b917-69f8cbf6d7b0 | [
{
"content": "How many three-digit natural numbers have digits that sum to 13 and leave a remainder of 1 when divided by 4?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe three-digit natural numbers with digits su... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 7bd935f5-cfef-4008-b139-657db1e1506c | [
{
"content": "Find the nth derivative of \\( f(x) = \\frac{x^n}{1 - x} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe nth derivative of \\( f(x) = \\frac{x^n}{1 - x} \\) is given by \\( \\frac{n!}{(1 - x)^{n+... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 83dc3d80-867e-48cc-8644-c94f3d6c439f | [
{
"content": "Find all the positive divisors of the integers:\ni) \\( A = p^k \\), where \\( p \\) is a prime number and \\( k \\) is a positive integer.\nii) \\( B = p^k \\cdot q^l \\), where \\( p, q \\) are positive prime numbers with \\( p \\neq q \\) and \\( k, l \\) are positive integers.\niii) \\( C = 19... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | da0cf3c2-5193-4cf1-860e-b51897df0f84 | [
{
"content": "Evaluate the integral $\\displaystyle \\int^{\\infty}_{0}\\sin(x^2)dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe integral \\(\\int_{0}^{\\infty} \\sin(x^2) dx\\) is a standard Fresnel integral... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 2643d7d5-a7f1-4935-9a19-3019db316140 | [
{
"content": "Given that \\(\\sin A + \\sin B = 1\\) and \\(\\cos A + \\cos B = 0\\), find the value of \\(12 \\cos 2A + 4 \\cos 2B\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nGiven the equations \\(\\sin A + \... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 0f6d7264-59f0-4735-963d-4d024507d712 | [
{
"content": "The regular octagon \\( ABCDEFGH \\) has an area of \\( n \\). Let \\( m \\) be the area of quadrilateral \\( ACEG \\). Calculate \\( \\frac{m}{n} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | e2956af9-b34b-4043-8378-ede3fc36104c | [
{
"content": "Solve the equation $x(x^{2}+11) + 3(x^{2}-3) + (x-11) \\sqrt{3-x} = 0$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation to solve is \\(x(x^2 + 11) + 3(x^2 - 3) + (x - 11) \\sqrt{3 - x} = 0\\)... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 85d3b4b6-a5b6-410c-86af-53682209e737 | [
{
"content": "Find all values of \\( n \\) such that the equation \\( x^3 + y^3 + z^3 = n(x^2 y^2 z^2) \\) has non-trivial solutions in positive integers.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation \\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 66e86da1-fc54-4971-8eef-a7c5d065f0ac | [
{
"content": "Evaluate the integral \\( \\int_0^{\\frac{\\pi}{2}} (x \\cos x + \\sin^2 x) \\sin x \\, dx \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe integral to evaluate is \\( \\int_0^{\\frac{\\pi}{2}} (x... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | ecd2b77c-108e-427d-8629-c0982d095699 | [
{
"content": "Suppose \\( A = [a_{ij}] \\in \\mathbb{R}^{n \\times n} \\) has the property that there exist constant real numbers \\( c_1, c_2, \\cdots, c_n \\) such that\n\\[ \\sum_{i=1}^k a_{ij} = c_k, \\text{ for all } 1 \\leq j \\leq k \\leq n. \\]\nDetermine all eigenvalues of \\( A \\).\nPlease reason ste... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | f8f6a5e4-f5a2-46da-b13b-7ec80a4b0b19 | [
{
"content": "Find all primes \\( p < q < r \\) such that \\( 25pq + r = 2004 \\) and \\( pqr + 1 \\) is a perfect square.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe primes \\(p\\), \\(q\\), and \\(r\\) satisf... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | dd9f82e0-8599-4153-8db3-1a7ed1692237 | [
{
"content": "Given two sinusoids with frequencies of $8 \\text{ kHz}$ and $3.5 \\text{ kHz}$, is the function obtained by summing these two sinusoids periodic? If so, what is the period of the resulting function?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | eebc2658-77d3-458a-97fc-10be798908cd | [
{
"content": "Solve the system of equations $x + y + z = 1$ and $xyz = 1$ where $x, y, z$ are complex numbers with absolute value equal to $1$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe system of equations is... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 755a1036-c6de-4650-b102-79295219c4f4 | [
{
"content": "Determine all positive integers that are equal to 300 times the sum of their digits.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe positive integers that satisfy the condition of being equal to 300 ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 84214e90-ddd4-4f15-919b-43efa5d55975 | [
{
"content": "A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 335e3b92-7061-4766-9939-275494c6ab67 | [
{
"content": "Calculate $\\lim_{n\\to \\infty} \\sqrt[n]{{nk}\\choose{n}}$, where $k$ is an arbitrarily fixed integer greater than $1$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nTo compute \\(\\lim_{n\\to \\infty... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | b07cc1d5-c3bd-4448-9a44-2cb71bd9e59b | [
{
"content": "Without using a calculator, determine which is greater: $\\sin 28^\\circ$ or $\\tan 21^\\circ$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nTo determine which is greater between \\(\\sin 28^\\circ\\) ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | e91be8a0-1b54-4902-99a6-49a03efc3ab5 | [
{
"content": "For certain pairs $(m, n)$ of positive integers with $m \\ge n$, there are exactly 50 distinct positive integers $k$ such that $|\\log m - \\log k| < \\log n$. Find the sum of all possible values of the product $mn$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"r... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 73491c2c-b339-48a8-8596-5707b2223307 | [
{
"content": "Let $n$ be a positive integer. Ana arranges $2n$ cups in a row on a table, each facing upside-down. She places a ball under one cup and makes a hole in the table under another cup. Banana gives a finite sequence of commands to Ana, where each command consists of swapping two adjacent cups in the r... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | c134379a-b83f-4532-9616-0b4f8cf0015f | [
{
"content": "In the complex plane, let points \\( A(x) \\), \\( B(y) \\), and \\( C(z) \\) be such that \\( |x| = |y| = |z| = m \\) where \\( m \\in \\mathbb{R}^+ \\), and \\( m^2 (x + y + z) = xyz \\in \\mathbb{R} \\). Find the area of triangle \\( ABC \\).\nPlease reason step by step, and put your final answ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | e2bd671c-b2d2-47f3-b60d-a6f7932cff06 | [
{
"content": "Find all pairs \\((m, n) \\in \\mathbb{N}^2\\) such that \\(n^{n^n} = m^m\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation to solve is \\(n^{n^n} = m^m\\) for pairs \\((m, n) \\in \\mathbb... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | b16e531d-e766-4fe8-bd68-13de7a9f1932 | [
{
"content": "Consider a sequence of integers \\(a_1, a_2, a_3, \\ldots\\) where \\(a_1 > 2\\). The sequence is defined by \\(a_{n+1} = \\frac{a_n(a_n - 1)}{2}\\). For what values of \\(a_1\\) are all terms of the sequence odd?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 2469ad83-7334-47a9-8a00-123b55812add | [
{
"content": "Given 8 piles of bricks with different amounts of bricks, each pile can be removed and its bricks can be scattered to the other piles so that the remaining piles have the same number of bricks. What is the smallest possible number of bricks in the biggest pile?\nPlease reason step by step, and put... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 6947058d-b59c-498b-af59-7406de67308d | [
{
"content": "Given that \\( n + m = 2014 \\), find the maximum and minimum values of \\( n! \\cdot m! \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nGiven that \\(n + m = 2014\\) and \\(n\\), \\(m\\) are non-neg... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 59e43aba-9475-4942-af8f-7d11a6b1904e | [
{
"content": "A word is a combination of 8 letters, each either A or B. Let x and y be two words that differ in exactly 3 places. How many words differ from each of x and y in at least 5 places?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content":... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 9d795992-ae27-4c65-9eea-1a30b0ba5ec0 | [
{
"content": "A particular right prism has a rectangular octagonal base with each base edge measuring 4 cm and a height of 3 cm. Its volume can be expressed in the form \\(a(b + \\sqrt{c})\\) cubic cm, where \\(c\\) is not divisible by the square of a prime. What is the value of \\(a + b + c\\)?\nPlease reason ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 7a18cc3d-925a-4b77-b1d3-e7f27282eeac | [
{
"content": "Solve the equation \\(\\dfrac{1}{x+2009} + \\dfrac{2010}{y+2010} = 1\\) for natural numbers \\(x\\) and \\(y\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation to solve is \\(\\dfrac{1}{x+20... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | b6108e2b-cb0d-4e66-b608-31a324a9a07a | [
{
"content": "Given a triangle with vertices \\((x_1, y_1)\\), \\((x_2, y_2)\\), and \\((x_3, y_3)\\), find the coordinates of the incenter of the triangle.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe incenter ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 09ff5c54-a9d5-4f2b-9ea2-9cfe78515250 | [
{
"content": "Solve the equation in real numbers:\n$$[x] + [2x] + [3x] + \\cdots + [2017x] = 1 + 2 + 3 + \\cdots + 2017$$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation to solve is \\([x] + [2x] + [3x] + ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 709bbc56-758d-4ba9-bfed-1984fee7ca3d | [
{
"content": "A pipe is being carried down a hallway that is 8 ft wide. At the end of the hallway, there is a right-angled turn into a narrower hallway 7 ft wide. Find the length of the longest pipe that can be carried around the corner. Round your answer to two decimal places.\nPlease reason step by step, and ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 236cfdd9-f4bc-448f-b57d-e002342dfe87 | [
{
"content": "In parallelogram $ABCD$, angles $B$ and $D$ are acute while angles $A$ and $C$ are obtuse. The perpendicular from $C$ to $AB$ and the perpendicular from $A$ to $BC$ intersect at a point $P$ inside the parallelogram. If $PB=700$ and $PD=821$, what is $AC$?\nPlease reason step by step, and put your ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | f8ad9798-62a7-46df-8615-dd0a3a3c52b4 | [
{
"content": "Find the coefficient of \\( a^8 b^4 c^9 d^9 \\) in the expansion of \\( (ab(c+d) + cd(a+b))^{10} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe expression \\((ab(c+d) + cd(a+b))^{10}\\) simplifi... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 8d496f7f-dbab-45c0-b517-b89478789946 | [
{
"content": "Find all triples of positive integers \\((x, y, z)\\) such that \\(2015x^3 + y^3 = 2014z^3\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation to solve is \\(2015x^3 + y^3 = 2014z^3\\) for po... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | dbf511c7-5798-42ee-9d09-2248f7825ca0 | [
{
"content": "Determine the value of the expression $ \\sqrt {5 + \\sqrt {5^2 + \\sqrt {5^4 + \\sqrt {5^8 + \\ldots}}}}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe expression is an infinite nested radical: \\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 4fd18017-0f7d-47a1-9eb9-00e43ad0fcf6 | [
{
"content": "Find \\( \\lim_{x \\to 1} \\frac{\\ln(x-1) + \\tan\\left(\\frac{\\pi x}{2}\\right)}{\\cot(\\pi x)} \\)\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe limit is evaluated as \\(x\\) approaches 1 from t... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 41ea3740-7114-4d67-a4bf-213a966dbdde | [
{
"content": "What is the largest $n$ for which there exists a convex $n$-gon whose diagonal lengths are at most two different values?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe largest \\(n\\) for which there... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 2ccf0d1b-7242-4c4b-8590-ff059da80715 | [
{
"content": "Find the number of solutions in non-negative reals to the following system of equations:\n\\[\n\\begin{cases}\nx_1 + x_n^2 = 4x_n \\\\\nx_2 + x_1^2 = 4x_1 \\\\\n\\vdots \\\\\nx_n + x_{n-1}^2 = 4x_{n-1}\n\\end{cases}\n\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | c217d436-49fe-41ed-bffb-785359076471 | [
{
"content": "A right-angled triangle is inscribed in the parabola $y = x^2$, with its hypotenuse parallel to the $x$-axis. What can be the altitude of the triangle drawn to the hypotenuse?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<th... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | ccbba80e-135f-404f-956b-ce0d64d09648 | [
{
"content": "Consider a sequence \\(a_1, a_2, \\cdots, a_{100}\\) of integers where \\(a_1 = 0\\) and \\(a_{100} = 0\\). For each term \\(a_i\\) (where \\(2 \\leq i \\leq 99\\)), \\(a_i\\) is larger than the average of its neighbors \\(a_{i-1}\\) and \\(a_{i+1}\\). What is the smallest possible value for the t... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 1875da7b-be60-4d4e-9ab6-98d9c52fdc04 | [
{
"content": "In a cyclic quadrilateral, each side has a length of either $6$ or $8$, and one of the diagonals has a length of $10$. Find the radius of its circumscribed circle.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</th... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | b5e494e9-3c83-4d84-8c1c-dba4ff66f773 | [
{
"content": "Given a triangle \\( \\triangle ABC \\) with \\( \\angle ACB = 60^\\circ \\) and \\( AC = BC \\). Point \\( M \\) is such that \\( AM = \\sqrt{2} \\), \\( BM = 2 \\), and \\( \\angle AMC = 15^\\circ \\). Find the length of \\( CM \\).\nPlease reason step by step, and put your final answer within \... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 57215f6c-b07a-4bb8-ba8c-e95db666eb72 | [
{
"content": "Solve the system of equations for \\(a, b, c \\in \\mathbb{R}\\):\n\n\\[\n\\begin{aligned}\na^2 + b^2 + c^2 &= \\frac{5}{3} \\\\\nabc &= 1\n\\end{aligned}\n\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | c2cbe525-9754-41c5-a937-f0e5f6685c28 | [
{
"content": "What is the greatest integer of the product \\((1+1)(1+\\frac{1}{2})(1+\\frac{1}{4})(1+\\frac{1}{8})(1+\\frac{1}{16}) \\cdots (1+\\frac{1}{1024})(1+\\frac{1}{2048})\\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | fad2d2d3-857d-4b67-9d9f-826618590123 | [
{
"content": "Determine the remainder when \\( a_{83} = 6^{83} + 8^{83} \\) is divided by 49.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nTo determine the remainder when \\(a_{83} = 6^{83} + 8^{83}\\) is divided by... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 0e6f1526-a2c4-4370-bffb-ec651ec06c1f | [
{
"content": "Given that \\( x^2 + y^2 = \\sqrt{3} \\), find the minimum value of \\( \\frac{3}{xy} + \\frac{x}{y} - \\frac{y}{x} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nGiven the constraint \\(x^2 + y^2 =... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 64ab145f-284a-4b37-8213-3478d18f6125 | [
{
"content": "Find the largest natural number \\( n \\) such that \\( 4^n + 4^{1004} + 4^{88} \\) is a perfect square.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe expression \\(4^n + 4^{1004} + 4^{88}\\) is rew... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | d76f7b33-8c1e-46de-870e-06638690c7a7 | [
{
"content": "$A$ and $B$ travel around a circular track at uniform speeds in opposite directions, starting from diametrically opposite points. If they start at the same time, meet first after $B$ has traveled $100$ yards, and meet a second time $60$ yards before $A$ completes one lap, then what is the circumfe... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | eaa17062-7cf5-4a2d-a507-bae3e384513c | [
{
"content": "Let \\( P(x) \\) be a polynomial of degree 2010. What is the maximum degree of the polynomial \\( P(x-1) - 3P(x) + 3P(x+1) - P(x+2) \\)?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe expression \\(P... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 77d6867f-b44b-4ac4-95ba-14ad89bf580b | [
{
"content": "What is the difference between the largest and smallest value for \\( \\text{lcm}(a, b, c) \\), where \\( a, b \\), and \\( c \\) are distinct positive integers between 1 and 10, inclusive?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | a4182321-806e-4a08-a4ca-aad9d4520b2d | [
{
"content": "Solve the system:\n\\[ x^3 + x(y - z)^2 = 2 \\]\n\\[ y^3 + y(z - x)^2 = 30 \\]\n\\[ z^3 + z(x - y)^2 = 16 \\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe system of equations is solved as follows:\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | f3a2f166-ff05-4d38-8941-5a12cf3e3b21 | [
{
"content": "Find all functions \\( f\\colon \\mathbb{R}\\to\\mathbb{R} \\) such that \\( f(f(x)) - 4f^3(x) + 4f(x) = -12x^3 + 21x - 10 \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe functional equation to s... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 9e49d8ea-20a6-4447-bd4b-026b6e1539ca | [
{
"content": "Let $a, b, c$, and $m$ be positive real numbers. Find for which $m$, independently of $a, b$, and $c$, at least one of the following three equations has real roots:\n\\[ ax^2 + bx + cm = 0, \\]\n\\[ bx^2 + cx + am = 0, \\]\n\\[ cx^2 + ax + bm = 0. \\]\nPlease reason step by step, and put your fina... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | add119fa-0233-434d-80f0-8d6b5cea765e | [
{
"content": "Evaluate \\(\\lim_{n\\to\\infty} nI_n^2\\) where \\(I_n = \\int_0^{\\frac{\\pi}{2}} \\sin^n \\theta \\, d\\theta\\) for \\(n = 0, 1, 2, \\ldots\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe limi... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 6aab3e0e-42cb-4d7a-b372-cba7428f1808 | [
{
"content": "Solve the equation $\\lfloor x \\rfloor \\cdot \\lfloor y \\rfloor = x + y$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation to solve is \\(\\lfloor x \\rfloor \\cdot \\lfloor y \\rfloor = x ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 03083c8e-78f4-40ea-88e1-e8930aa5b0b7 | [
{
"content": "In triangle \\(ABC\\) with \\(AB \\neq AC\\), point \\(I\\) is the incenter. The lines \\(BI\\) and \\(CI\\) intersect sides \\(AC\\) and \\(AB\\) at points \\(D\\) and \\(E\\) respectively. Determine all possible angles \\(\\angle BAC\\) such that \\(DI = EI\\).\nPlease reason step by step, and p... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | fb3f0dc3-168e-454c-ab0b-7e1798e162aa | [
{
"content": "Solve for \\( m \\) such that \\( K(m,3) = 64m^3 + 702046 \\), where \\( K(m,n) \\) is the smallest natural number exceeding \\( (\\sqrt{m+3} + \\sqrt{m+2})^{2n} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n<... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 576d61fd-b2db-47b2-ae04-8d8ccc77ab72 | [
{
"content": "Let \\(a, b, c, d\\) be the roots of the equation \\(t^4 - t^3 - 4t^2 + t + 1 = 0\\). Solve the system of equations:\n\n\\[\n\\begin{cases}\n\\frac{x}{a} + \\frac{y}{a-1} + \\frac{z}{a+1} + \\frac{w}{a-2} = a^2 \\\\\n\\frac{x}{b} + \\frac{y}{b-1} + \\frac{z}{b+1} + \\frac{w}{b-2} = b^2 \\\\\n\\fra... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 279ee59b-8a49-414b-934c-4eb3ec32f09a | [
{
"content": "Find all prime numbers \\( p \\) and \\( q \\) such that \\( pq \\) divides \\( (5^p - 2^p)(5^q - 2^q) \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe prime pairs \\((p, q)\\) that satisfy the co... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 2906d248-b905-4267-a89a-f9e4c2ddee6f | [
{
"content": "Find all solutions $(r,s,t) \\in \\mathbb{N}^3$ of the equation $1 + 3^r + 3^s = 7^t$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation to solve is \\(1 + 3^r + 3^s = 7^t\\) for natural number... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | ddd6705f-4c2e-46d3-afd7-ddeaab88d3b9 | [
{
"content": "Given that \\( f(xy) = f(x) + f(y) + 1 \\) for \\( x, y > 0 \\) and \\( f(2) = 0 \\), find \\( f(2018) \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe functional equation is \\(f(xy) = f(x) + f(y... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 4cb44595-55af-4cee-abc7-bf20bacbc095 | [
{
"content": "Solve the system of equations for \\( x, y, z \\in \\mathbb{R} \\):\n\\[\n\\begin{cases} \n\\sqrt{x+y} + \\sqrt{z} = 7 \\\\\n\\sqrt{x+z} + \\sqrt{y} = 7 \\\\\n\\sqrt{y+z} + \\sqrt{x} = 5\n\\end{cases}\n\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 06a0fb7e-258c-4fe2-a7e7-62a9b24e886f | [
{
"content": "What is the value of $$\\sum_{b=5}^\\infty \\frac{15b^2+68b+120}{2^b(b^4+64)}$$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe sum \\(\\sum_{b=5}^\\infty \\frac{15b^2+68b+120}{2^b(b^4+64)}\\) is eva... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | fc5e3b4a-b57e-4902-b518-09386baa25ee | [
{
"content": "Find the volume of a doughnut (torus) with an inner diameter of 2 cm and a boundary diameter of 2 cm. Generalize the formula for the volume of a torus given its inner and boundary diameters.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 3dfd2b63-4bbe-4473-8f28-59d14cd78590 | [
{
"content": "Find all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that for all \\( x, y \\in \\mathbb{R} \\), the equation \\( f(xf(y) + f(x)) = 2f(x) + xy \\) holds.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</t... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 6d617988-6c5a-427d-980f-3d1aa70d8d3b | [
{
"content": "Given a triangle \\(ABC\\), locate its orthocenter using only a compass and an unmarked ruler. No other tools are allowed (besides a pencil).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nTo locate the ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 64c778b0-6b67-4995-800b-86dc786bb030 | [
{
"content": "For the set \\( S_n = \\{1, 2, \\ldots, n\\} \\), find the maximum value of \\( m \\) such that there exist \\( m \\) different subsets \\( A_1, A_2, \\ldots, A_m \\) of \\( S_n \\) where for every \\( i, j = 1, 2, \\ldots, m \\), the union \\( A_i \\cup A_j \\) is not equal to \\( S_n \\).\nPleas... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 91dfe08a-3dd4-4410-9d8e-7fd6890be226 | [
{
"content": "In $\\triangle ABC$, points $M$, $I$, and $H$ are the feet of the median, bisector, and height, respectively, drawn from $A$. Given that $BC = 2$, $MI = 2 - \\sqrt{3}$, and $AB > AC$, determine $\\frac{AB}{AC}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role":... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 3351864f-c3cf-448a-a5a4-ef120514b425 | [
{
"content": "Find all functions \\( f: \\mathbb{Z} \\longrightarrow \\mathbb{R} \\) such that for every \\( k \\in \\mathbb{Z} \\setminus \\{0\\} \\),\n\\[ \\sum_{s \\in \\mathbb{Z}} f(s)f(s+k) = 0 \\quad \\text{and} \\quad \\sum_{s \\in \\mathbb{Z}} f(s)f(s) = 1. \\]\nPlease reason step by step, and put your ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | e0df3758-3c80-469b-8e60-ad16c910204a | [
{
"content": "Given the matrix \\( A = \\begin{pmatrix} 2 & 1 & 0 \\\\ 0 & 2 & 0 \\\\ 2 & 3 & 1 \\end{pmatrix} \\) and the minimal polynomial \\( m(x) = (x-2)^2 (x-1) \\), find the matrix \\( P \\) such that \\( AP = PJ \\), where \\( J \\) is the Jordan form of \\( A \\).\nPlease reason step by step, and put y... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 48876ccb-9607-4b09-906c-0bac32e385e8 | [
{
"content": "Find all positive integers that have an even number of nice representations, where a nice representation of a positive integer \\( n \\) is defined as a sum of powers of 2 with at most two equal powers in the sum.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | b51280d1-da6c-490a-9340-d870f781d23d | [
{
"content": "Compare \\( A = \\frac{2007^{2006} + 1}{2007^{2007} + 1} \\) and \\( B = \\frac{2007^{2007} + 1}{2007^{2008} + 1} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nTo compare \\( A = \\frac{2007^{2006}... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | ff090ac6-9b0f-4746-a385-ee71485ff348 | [
{
"content": "Given a square \\(ABCD\\), let \\(P, Q, R\\), and \\(S\\) be four variable points on the sides \\(AB, BC, CD\\), and \\(DA\\), respectively. Determine the positions of the points \\(P, Q, R\\), and \\(S\\) for which the quadrilateral \\(PQRS\\) is a parallelogram.\nPlease reason step by step, and ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | e8dc8fee-0cf2-4528-b0b1-c36115c2b815 | [
{
"content": "Use the Taylor Series found in part (a) to find the limit as \\( x \\) approaches 0 of \\( \\frac{1 - x^2 - f(x)}{x^4} \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe Taylor series expansion of \... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | d86f8611-406c-4015-8311-7469a257f6dc | [
{
"content": "Given positive integers \\( v, e, \\) and \\( f \\) satisfying \\( v - e + f = 2 \\), how can one construct a cell structure on \\( S^2 \\) having \\( v \\) 0-cells, \\( e \\) 1-cells, and \\( f \\) 2-cells?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "us... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | fc41990b-1d01-4cc5-8638-a8fe2644b9f9 | [
{
"content": "If $z$ is a complex number such that $z^{23}=1$, find the value of $\\displaystyle \\sum^{22}_{k=1}\\frac{1}{1+z^{8k}+z^{16k}}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe complex number \\(z\\) ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 4038ba9f-6510-41cd-bee5-c9b86af2fc9c | [
{
"content": "Given various trapezoids whose two nonparallel sides and the smaller base are equal to $a$. Find the value of the greater base of the trapezoid which has the greatest area.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 1c09d2d8-1d5e-42c8-871a-7da50d297558 | [
{
"content": "Evaluate the integral $\\int_{0}^{\\frac{\\pi}{4}} \\cos^{\\frac{3}{2}}(2x) \\cos(x) \\, dx$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nTo evaluate the integral \\(\\int_{0}^{\\frac{\\pi}{4}} \\cos^... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 314c3abf-0ab1-4638-9967-867526e46383 | [
{
"content": "Let A be the point (7,4) and D be (-5,-3). What is the length of the shortest path ABCD, where B is a point (x, 2) and C is a point (x, 0)? This path consists of three connected segments, with the middle one vertical.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | fa96221c-e2aa-4c76-b10a-739fa0afe29c | [
{
"content": "For \\( n \\geq 2 \\), let \\( a_n x + b_n \\) be the remainder when \\( x^n \\) is divided by \\( x^2 - 6x - 12 \\). Find, for each \\( n \\), all prime numbers that are common divisors of \\( a_n \\) and \\( b_n \\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | f6bbde51-61b3-416d-81ac-f221ee7eb7bd | [
{
"content": "Given complex numbers \\( z_1, z_2, z_3 \\) satisfying \\( |z_1| \\leq 1 \\), \\( |z_2| \\leq 1 \\), \\( |z_3| \\leq 1 \\), and \\( z_1 + z_2 + z_3 = 0 \\), find the maximum value of \\( |z_1 \\overline{z_2} + z_2 \\overline{z_3} + z_3 \\overline{z_1}| \\).\nPlease reason step by step, and put you... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 93e96799-12ce-4342-97ad-ea1f8cb41319 | [
{
"content": "Solve the following equations and inequalities: $\\sqrt {\\frac{x^2-2x-2}{x^2+4x+2}}+\\sqrt {\\frac{x^2+4x+2}{x^2-2x-2}}=2$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe equation to solve is \\(\\s... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 0ced0e55-7ced-4141-b803-70b43ad2641b | [
{
"content": "Find the sum of the squares of the digits of the least positive integer having 72 positive divisors.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe least positive integer with exactly 72 positive div... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 276cd496-4fab-4514-9669-ea0934c086f1 | [
{
"content": "Given three non-negative real numbers \\(a, b, c\\) such that \\(a + b + c = 6\\), find the maximal value of \\(\\sqrt[3]{a^2 + bc} + \\sqrt[3]{b^2 + ca} + \\sqrt[3]{c^2 + ab}\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": ... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 5eaa6157-5611-411c-a4da-6a9fd466b32b | [
{
"content": "Find all positive integers $n$ such that the sum of the digits of $2^n$ is equal to the sum of the digits of $5^n$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</think>\n\nThe only positive integer \\(n\\) that s... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | ef7a32cd-c9dd-4140-b203-7392bef4ffe8 | [
{
"content": "Let \\(a, b, x, y\\) be real numbers such that \\(ax + by = 1\\), \\(ax^2 + by^2 = 2\\), \\(ax^3 + by^3 = 8\\), and \\(ax^5 + by^5 = 100\\). Find \\(ax^4 + by^4\\).\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\n\n</t... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | d1aeae05-745c-4390-a29e-b487bcf2e228 | [
{
"content": "Given a set $S$ of 5 points in the plane, no three of which are collinear, let $A(S)$ be the largest area of a triangle formed by any three points in $S$, and $a(S)$ be the smallest area of a triangle formed by any three points in $S$. What is the minimum possible value of the ratio $A(S)/a(S)$?\n... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | bb6a28db-5e02-4f4c-a93b-0ca9e82bfd1f | [
{
"content": "Compute the limit\n\\[\n\\lim_{x \\to 1} \\left( \\frac{H_x}{x(x-1)} - \\frac{1}{(x-1)(2x-1)} \\right),\n\\]\nwhere \\( H_x \\) represents the fractional harmonic number.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "<think>\... | Nemotron-Post-Training-Dataset-v2/math | 0 |
DeepSeek-R1-0528 | 2f99c885-b365-490a-bc97-d97757487f70 | [
{
"content": "Solve the following system of equations for the components of $\\vec{E}$:\n\n\\[\nE_x=\\frac{D_x}{1+4\\pi\\left(\\chi_1+\\chi_k\\left(E_x^2+E_y^2+E_z^2\\right)\\right)}\n\\]\n\n\\[\nE_y=\\frac{D_y}{1+4\\pi\\left(\\chi_1+\\chi_k\\left(E_x^2+E_y^2+E_z^2\\right)\\right)}\n\\]\n\n\\[\nE_z=\\frac{D_z}{... | Nemotron-Post-Training-Dataset-v2/math | 0 |
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