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test2_CROHME2016

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\[\sin(t)\]

\[r= \sqrt{x_{6}^{2}+x_{7}^{2}+x_{8}^{2}+x_{9}^{2}}\]

\[L \sin \theta\]

\[( \sqrt{3}- \sqrt{2})<2c<( \sqrt{3}+ \sqrt{2})\]

\[\lim_{r \rightarrow \infty}e^{2r}(n-H(r))=2n\]

\[z= \tan x\]

\[- \frac{n}{2}b- \frac{m}{2}b^{-1}\]

\[\cos kx\]

\[y_{1}y_{2}y_{3}y_{4}y_{5}\]

\[7+5+3+3=18=3 \times(5+1)\]

\[\frac{n-1}{2}- \frac{-n-1}{2}=n\]

\[B^{a \beta}(x)=A^{a \beta}(x)\]

\[\sum_{a}p_{a}\]

\[(- \frac{1}{3},- \frac{1}{3},- \frac{1}{3},- \frac{1}{3},- \frac{1}{3}, \frac{4}{3}, \frac{2}{3}, \frac{2}{3})\]

\[x_{1}x_{d+1}+ \ldots+x_{d}x_{2d}\]

\[(1)+(6+6)+(1+3 \times 6)=32\]

\[\frac{1}{6}(j+1)(j+2)(2j+3)\]

\[-x_{9}\]

\[E^{ \alpha}(x_{1}( \frac{x_{2}}{x_{1}})^{2})=2x_{2}\]

\[1+ \frac{1}{z} \sin z \cos(z+2 \alpha_{1})=2 \int_{0}^{1}dx \cos^{2}(zx+ \alpha_{1})\]

\[10^{ \sqrt{N \log N}}\]

\[T_{0}\]

\[9 \times 9\]

\[ax=bandya=b\]

\[\int d^{10}x\]

\[\sqrt{l_{1}}+ \sqrt{l_{2}} \geq \sqrt{l_{3}}\]

\[R(x)= \frac{1}{ \sqrt{n+ \frac{q}{2 \pi} \cos^{2}(nx)}}\]

\[S_{eff}^{F}[ \phi^{ \prime}]+S_{1}[ \phi^{ \prime}]=S_{eff}^{F^{ \prime}}[ \phi^{ \prime}]\]

\[V^{ab}=V^{(a+1)(b+1)}\]

\[[x_{2}]-[x_{1}]\]

\[\sin \theta \cos \theta N_{3}\]

\[\frac{4}{135} \sqrt{5}\]

\[x_{2}<x<x_{1}\]

\[t^{ \frac{1}{2}}-t^{- \frac{1}{2}}\]

\[p=1 \div m\]

\[a,b \ldots 0 \div d-1\]

\[1.1+0.01i\]

\[S^{m}\]

\[\frac{(ga)^{4}}{4!} \frac{4 \times 3}{2!} \times 2^{4} \times 2= \frac{(2ga)^{4}}{2!}\]

\[-2+ \frac{v-2}{v} \log(1-v)\]

\[x^{u}dx^{u}=dx^{u}x^{e}\]

\[k= \sum_{i}k_{i}=- \sum_{y}k_{y}\]

\[y=y(x)\]

\[z^{a}=x^{a+3}+ix^{a+6}\]

\[f( \pm \pi, \pm \pi, \pm \pi)=-f( \pm \pi, \pm \pi, \pm \pi)=0\]

\[a_{ii}= \frac{1}{2}( \frac{(m^{i})^{2}}{6}+m^{i})\]

\[x_{-n}= \sqrt{n}(a-ib)\]

\[\sqrt{1+rm_{a}}\]

\[-2^{ \frac{1}{4}}( \frac{5- \sqrt{5}}{5+ \sqrt{5}})^{ \frac{3}{4}}\]

\[u_{ab}=n_{ab}+u_{a}u_{b}\]

\[\frac{7}{6}\]

\[B_{23}^{ \infty}= \tan \theta\]

\[B=A- \frac{ \sin^{2} \theta_{1}}{ \cos^{2} \theta_{1}}\]

\[- \frac{ \alpha^{2}}{ \alpha^{2}+1}= \frac{1}{ \alpha^{2}+1}\]

\[e^{-A}A^{A}\]

\[[c_{1}]+[c_{2}]=[c_{1}+c_{2}]\]

\[x^{2}+x^{3}+x^{5}=a+b\]

\[y= \tan \frac{ \mu}{2}\]

\[X_{1}X_{8}=X_{6}X_{7}\]

\[x+x^{t}\]

\[8 \sin( \pi/14) \sin(3 \pi/14) \cos( \pi/7)=1\]

\[x^{ \pm j}= \frac{1}{ \sqrt{2}}(x^{2j+2} \pm ix^{2j+3})\]

\[\sum a_{n}(c_{n}+(-1)^{n}c_{-n})\]

\[x^{-1} \frac{d^{n-1}}{dx^{n-1}}\]

\[\frac{1}{x^{6}}\]

\[e^{ \pm \frac{1}{ \sqrt{2}}x}\]

\[- \infty<x< \infty\]

\[(10+2)-(6+6)-(2+10)\]

\[\sqrt{8 \pi}\]

\[y(r)=7r^{ \frac{73}{95}}+5r^{ \sqrt{5}}+3r^{ \pi}+r^{2 \sqrt{5}}+3r^{ \frac{77}{5}}\]

\[[a] \times[a] \times[b]\]

\[P_{m}\]

\[-0.988\]

\[x^{5}=- \sqrt{ \frac{2}{3}} \frac{1}{ \beta- \alpha} \log \frac{ \alpha+ \beta}{2 \alpha}\]

\[v=( \tan y_{0})u\]

\[| \frac{ \cos(x)-1}{x^{2}}|=| \frac{ \cos(|x|)-1}{|x|^{2}}|\]

\[z= \sqrt{ \frac{m}{2}}(x+iy)\]

\[\sum_{k=1}^{n-1}c_{k}c_{n-k}=c_{n+1}-2c_{n}\]

\[x= \cos(q)\]

\[y_{i}^{2}=x_{i}(x_{i}-1)(x_{i}-a_{i})\]

\[f((n+4)b)=f(nb)\]

\[4 \sin^{2}( \frac{1}{2}k \theta p)=2(1+ \cos(k \theta p))\]

\[B \rightarrow \tan \theta\]

\[-19.9469\]

\[P^{x}P^{x}\]

\[\int_{0}^{1}dyX(y)\]

\[\sqrt{2(2+ \sqrt{2})}\]

\[\frac{1}{3!}( \frac{3 \sqrt{3}}{4})^{3}\]

\[y=2x- \frac{c_{i}+c_{j}}{2}\]

\[\frac{7}{16}+7\]

\[\sum \sum_{b<a}^{N} \lambda_{a} \lambda_{b}= \sum_{a=1}^{N}r_{a}q_{a}^{2}- \sum_{a=1}^{N}q_{a}^{2} \sum_{b=1}^{N}r_{b}+ \sum \sum_{b<a}^{N}r_{b}r_{a}\]

\[\frac{N^{ \frac{7}{5}}}{g_{YM}^{ \frac{6}{5}}} \frac{1}{|x|^{ \frac{9}{5}}}\]

\[\beta_{2}+ \beta_{3}+ \beta_{4}+ \beta_{5}+ \beta_{6}+ \beta_{7}\]

\[\frac{2.5}{ \sqrt{2}}\]

\[Y_{0}+Y_{4}+Y_{8}+ \ldots\]

\[w(x)=x^{2a+1}e^{-nx}\]

\[X^{i}= \frac{1}{ \sqrt{2}}(X_{2i-1}+iX_{2i})\]

\[\frac{m}{s} \times \frac{n}{s}\]

\[n! \times n!\]

\[C_{xx}^{(1)}C_{xx}^{(2)}\]