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• 25 What aspects of math olympiads do you find still useful in your math research?
• 24 Prove $\int_0^{\pi/2}{\frac{1+2\cos 2x\cdot\ln\tan x}{1+\tan^{2\sqrt{2}} x}}\tan^{1/\sqrt{2}} x~dx=0$
• 18 Prove that $\sin x+\sin y=1$ does not have integer solutions
• 17 Proof $ \int_0^\infty \frac{\cos(2\pi x^2)}{\cosh^2(\pi x)}dx=\frac 14$?
• 13 Conjecture $\sum_{n=1}^\infty\frac{n^2}{(-1)^n \cosh(\pi n\sqrt{3})-1}=\frac{1}{12\pi^2}$
• 12 Prove that $\int_0^\infty\left(\arctan \frac1x\right)^2 \mathrm d x = \pi\ln 2$
• 10 Math competition problem, prove that $\int_{-\infty}^\infty e^{-\pi x^2 \left(\frac{\alpha +x}{\beta +x}\right)^2}dx=1~$ for $~0<\beta<\alpha$.
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