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Mathematics
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metamorphy
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Intuition is often a good guide but a bad prophet.
"Obvious" is what is easy to prove, not what is hard to refute.
Artificial intelligence is no match for natural stupidity.

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29
Prove that the quantity is an integer
Oct 7, 2018
26
Euler-Mascheroni constant in Bessel function integral
Jun 10, 2022
19
Prove $\sum_{n=1}^{\infty} \arctan\left(\frac{1}{F_n}\right) \arctan\left(\frac{1}{F_{n+1}}\right)=\frac{\pi^2}{8}$
Apr 4, 2021
18
Integral of Binomial Coefficient
Sep 26, 2018
17
Evaluate $\lim\limits_{n \to \infty}\frac{(-1)^n}{n!}\int_0^n (x-1)(x-2)\cdots(x-n){\rm d}x$
Jul 4, 2020
17
How to evaluate $\int_{-\infty}^{\infty}e^{x-n\sinh^2 x}\ dx$
Aug 13, 2021
16
Shannon entropy of a fair dice
Sep 14, 2018
16
Analytic continuation of $\Phi(s)=\sum_{n \ge 1} e^{-n^s}$
Aug 30, 2020
15
Maclaurin series of $1- \cos^{2/3} x$ has all coefficients positive
May 5, 2022
15
Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
Mar 7, 2020
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5
Behavior of $n\sqrt{3}-a_n\sqrt{n}$ as $n\to\infty$, where $a_{n+1}=a_n+n/(a_1+\dots+a_n)$