Prove that for any $n > 0$, if $a^n$ is even, then $a$ is even

Matrix with each cell equal to sum of its adjacent cells

What combination of inputs results in the largest output?

If $I_n=\int_0 ^1{\frac{x^{n+1}}{x+3}}dx$, prove $\lim_{n \to \infty} n I_n=\frac{1}{4}$

Closed form for the skew-harmonic sum $\sum_{n = 1}^\infty \frac{H_n \overline{H}_n}{n^2}$

A winning wager that loses over time

Torsion in abelian groups

Is $\Bbb R^2\times\Bbb S^2$ simply connected?

Name for quadratic functions with no linear term

Is there an efficient algorithm for iterating over binary strings where each of the reciprocal is enumerated exactly once?

Explaining a solution to a calculus problem.

Group cohomology of $PSU(n)$

Motivation of generalizing the theory of metric spaces to the theory of topological spaces

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