Top network posts

• 40 Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
• 28 If $x$ and $y$ are rational numbers and $x^5+y^5=2x^2y^2,$ then $1-xy$ is a perfect square.
• 22 Numbers are too large to show $65^{64}+64^{65}$ is not a prime
• 20 What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$
• 20 Show by substitution that $\int_0^{\pi} \frac{x\sin x}{1+\cos^2 x} \,\mathrm dx = \frac{\pi}{2}\int_0^{\pi} \frac{\sin x}{1+\cos^2 x} \,\mathrm dx$
• 19 Simplify $n^{\log\log n / \log n}$
• 15 Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
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