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test2_CROHME2016

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\[\sin(t)\]
\[r= \sqrt{x_{6}^{2}+x_{7}^{2}+x_{8}^{2}+x_{9}^{2}}\]
\[L \sin \theta\]
\[( \sqrt{3}- \sqrt{2})<2c<( \sqrt{3}+ \sqrt{2})\]
\[\lim_{r \rightarrow \infty}e^{2r}(n-H(r))=2n\]
\[z= \tan x\]
\[- \frac{n}{2}b- \frac{m}{2}b^{-1}\]
\[\cos kx\]
\[y_{1}y_{2}y_{3}y_{4}y_{5}\]
\[7+5+3+3=18=3 \times(5+1)\]
\[\frac{n-1}{2}- \frac{-n-1}{2}=n\]
\[B^{a \beta}(x)=A^{a \beta}(x)\]
\[\sum_{a}p_{a}\]
\[(- \frac{1}{3},- \frac{1}{3},- \frac{1}{3},- \frac{1}{3},- \frac{1}{3}, \frac{4}{3}, \frac{2}{3}, \frac{2}{3})\]
\[x_{1}x_{d+1}+ \ldots+x_{d}x_{2d}\]
\[(1)+(6+6)+(1+3 \times 6)=32\]
\[\frac{1}{6}(j+1)(j+2)(2j+3)\]
\[-x_{9}\]
\[E^{ \alpha}(x_{1}( \frac{x_{2}}{x_{1}})^{2})=2x_{2}\]
\[1+ \frac{1}{z} \sin z \cos(z+2 \alpha_{1})=2 \int_{0}^{1}dx \cos^{2}(zx+ \alpha_{1})\]
\[10^{ \sqrt{N \log N}}\]
\[T_{0}\]
\[9 \times 9\]
\[ax=bandya=b\]
\[\int d^{10}x\]
\[\sqrt{l_{1}}+ \sqrt{l_{2}} \geq \sqrt{l_{3}}\]
\[R(x)= \frac{1}{ \sqrt{n+ \frac{q}{2 \pi} \cos^{2}(nx)}}\]
\[S_{eff}^{F}[ \phi^{ \prime}]+S_{1}[ \phi^{ \prime}]=S_{eff}^{F^{ \prime}}[ \phi^{ \prime}]\]
\[V^{ab}=V^{(a+1)(b+1)}\]
\[[x_{2}]-[x_{1}]\]
\[\sin \theta \cos \theta N_{3}\]
\[\frac{4}{135} \sqrt{5}\]
\[x_{2}<x<x_{1}\]
\[t^{ \frac{1}{2}}-t^{- \frac{1}{2}}\]
\[p=1 \div m\]
\[a,b \ldots 0 \div d-1\]
\[1.1+0.01i\]
\[S^{m}\]
\[\frac{(ga)^{4}}{4!} \frac{4 \times 3}{2!} \times 2^{4} \times 2= \frac{(2ga)^{4}}{2!}\]
\[-2+ \frac{v-2}{v} \log(1-v)\]
\[x^{u}dx^{u}=dx^{u}x^{e}\]
\[k= \sum_{i}k_{i}=- \sum_{y}k_{y}\]
\[y=y(x)\]
\[z^{a}=x^{a+3}+ix^{a+6}\]
\[f( \pm \pi, \pm \pi, \pm \pi)=-f( \pm \pi, \pm \pi, \pm \pi)=0\]
\[a_{ii}= \frac{1}{2}( \frac{(m^{i})^{2}}{6}+m^{i})\]
\[x_{-n}= \sqrt{n}(a-ib)\]
\[\sqrt{1+rm_{a}}\]
\[-2^{ \frac{1}{4}}( \frac{5- \sqrt{5}}{5+ \sqrt{5}})^{ \frac{3}{4}}\]
\[u_{ab}=n_{ab}+u_{a}u_{b}\]
\[\frac{7}{6}\]
\[B_{23}^{ \infty}= \tan \theta\]
\[B=A- \frac{ \sin^{2} \theta_{1}}{ \cos^{2} \theta_{1}}\]
\[- \frac{ \alpha^{2}}{ \alpha^{2}+1}= \frac{1}{ \alpha^{2}+1}\]
\[e^{-A}A^{A}\]
\[[c_{1}]+[c_{2}]=[c_{1}+c_{2}]\]
\[x^{2}+x^{3}+x^{5}=a+b\]
\[y= \tan \frac{ \mu}{2}\]
\[X_{1}X_{8}=X_{6}X_{7}\]
\[x+x^{t}\]
\[8 \sin( \pi/14) \sin(3 \pi/14) \cos( \pi/7)=1\]
\[x^{ \pm j}= \frac{1}{ \sqrt{2}}(x^{2j+2} \pm ix^{2j+3})\]
\[\sum a_{n}(c_{n}+(-1)^{n}c_{-n})\]
\[x^{-1} \frac{d^{n-1}}{dx^{n-1}}\]
\[\frac{1}{x^{6}}\]
\[e^{ \pm \frac{1}{ \sqrt{2}}x}\]
\[- \infty<x< \infty\]
\[(10+2)-(6+6)-(2+10)\]
\[\sqrt{8 \pi}\]
\[y(r)=7r^{ \frac{73}{95}}+5r^{ \sqrt{5}}+3r^{ \pi}+r^{2 \sqrt{5}}+3r^{ \frac{77}{5}}\]
\[[a] \times[a] \times[b]\]
\[P_{m}\]
\[-0.988\]
\[x^{5}=- \sqrt{ \frac{2}{3}} \frac{1}{ \beta- \alpha} \log \frac{ \alpha+ \beta}{2 \alpha}\]
\[v=( \tan y_{0})u\]
\[| \frac{ \cos(x)-1}{x^{2}}|=| \frac{ \cos(|x|)-1}{|x|^{2}}|\]
\[z= \sqrt{ \frac{m}{2}}(x+iy)\]
\[\sum_{k=1}^{n-1}c_{k}c_{n-k}=c_{n+1}-2c_{n}\]
\[x= \cos(q)\]
\[y_{i}^{2}=x_{i}(x_{i}-1)(x_{i}-a_{i})\]
\[f((n+4)b)=f(nb)\]
\[4 \sin^{2}( \frac{1}{2}k \theta p)=2(1+ \cos(k \theta p))\]
\[B \rightarrow \tan \theta\]
\[-19.9469\]
\[P^{x}P^{x}\]
\[\int_{0}^{1}dyX(y)\]
\[\sqrt{2(2+ \sqrt{2})}\]
\[\frac{1}{3!}( \frac{3 \sqrt{3}}{4})^{3}\]
\[y=2x- \frac{c_{i}+c_{j}}{2}\]
\[\frac{7}{16}+7\]
\[\sum \sum_{b<a}^{N} \lambda_{a} \lambda_{b}= \sum_{a=1}^{N}r_{a}q_{a}^{2}- \sum_{a=1}^{N}q_{a}^{2} \sum_{b=1}^{N}r_{b}+ \sum \sum_{b<a}^{N}r_{b}r_{a}\]
\[\frac{N^{ \frac{7}{5}}}{g_{YM}^{ \frac{6}{5}}} \frac{1}{|x|^{ \frac{9}{5}}}\]
\[\beta_{2}+ \beta_{3}+ \beta_{4}+ \beta_{5}+ \beta_{6}+ \beta_{7}\]
\[\frac{2.5}{ \sqrt{2}}\]
\[Y_{0}+Y_{4}+Y_{8}+ \ldots\]
\[w(x)=x^{2a+1}e^{-nx}\]
\[X^{i}= \frac{1}{ \sqrt{2}}(X_{2i-1}+iX_{2i})\]
\[\frac{m}{s} \times \frac{n}{s}\]
\[n! \times n!\]
\[C_{xx}^{(1)}C_{xx}^{(2)}\]