name stringclasses 2
values | formal_statement stringclasses 2
values | informal_statement stringclasses 2
values | tags stringclasses 2
values | header stringclasses 2
values | split stringclasses 1
value |
|---|---|---|---|---|---|
putnam_2002_a6 | theorem putnam_2002_a6
(f : β β β β β)
(hf : β b : β, f b 1 = 1 β§ f b 2 = 2 β§ β n β Ici 3, f b n = n * f b (Nat.digits b n).length)
: {b β Ici 2 | β L : β, Tendsto (fun m : β => β n in Finset.Icc 1 m, 1/(f b n)) atTop (π L)} = putnam_2002_a6_solution :=
sorry | Fix an integer $b \geq 2$. Let $f(1) = 1$, $f(2) = 2$, and for each
$n \geq 3$, define $f(n) = n f(d)$, where $d$ is the number of
base-$b$ digits of $n$. For which values of $b$ does
\[
\sum_{n=1}^\infty \frac{1}{f(n)}
\]
converge? | ['analysis', 'number_theory'] | abbrev putnam_2002_a6_solution : Set β := sorry
-- {2}
| valid |
f2f_mathd_numbertheory_45 | theorem mathd_numbertheory_45 : Nat.gcd 6432 132 + 11 = 23 := by
| /-- What is the result when the greatest common factor of 6432 and 132 is increased by 11? Show that it is 23.-/
| ['number_theory'] | import Mathlib
import Aesop
set_option maxHeartbeats 0
open BigOperators Real Nat Topology Rat
| valid |
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