Is every group $G$ a subgroup of index $2$ of some $\tilde G$?

Given $4$ variables and $5$ pairwise products, find the $6$th pairwise product?

Nice integral $\int_{0}^{\infty}\frac{x\log(x)}{e^{x^2}+1}dx=?$

Minimising the area between a line and an exponential curve

How to evaluate a sum of square roots rounded to the nearest integer?

Homomorphisms from $\prod_{i\in\mathbb Z}\mathbb Z $ to $\oplus_{i\in\mathbb Z}\mathbb Z$ that fixes $\oplus_{i\in\mathbb Z}\mathbb Z$

When does the center of a set of points lie in the convex hull?

A possible solution to $\sqrt {5-x}=5-x^2$ (without taking square from both sides)

Solve $\sin 84^\circ \sin(54^\circ-x)=\sin 126^\circ \sin x$.

How many ideals contain $(x^2+1)$ in $\mathbb{Z}_4[x]$?

Methods to solve $\int _0^{\infty }\frac{x^{\frac{4}{5}}-x^{\frac{2}{3}}}{\ln \left(x\right)\left(x^2+1\right)}\:dx$

Why do $\frac{(e^{2x}-(e^x\cos x)^2)}{x^2}$ and $\left(\frac{e^x\sin x}{x}\right)^2$ give different numeric results?

Convex polygons that do not tile the plane individually, but together they do

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