 # Bach

Top Questions

## Suppose $\alpha, \beta>0$. Compute: $\int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx$

asked Oct 22, 2018 at 13:30

## Differentiability of $G(x)=\int_{\mathbb R} e^{tx}f(t)dt$ on $(0,1)$

asked Jul 20, 2019 at 14:07

## Suppose that $G$ is a group of order $924=2^2\cdot3\cdot7\cdot 11$. Prove that $G$ has an element of order $77$.

asked May 31, 2019 at 9:08

## What is the intuition behind the law of quadratic reciprocity?

asked Feb 6, 2020 at 0:30

## $f(z)=z^n+a_{n-1}z^{n-1}+\cdots+ a_0\in\mathbb Z[z]$ has all its roots on the unit circle. Prove that any root of $f(z)=0$ is a root of unity.

asked Aug 14, 2019 at 15:45

## Let $R$ be a p.i.d. and $A\in M_n(R)$. If $\det(A)=1$, prove or disprove that $A$ can be expressed as products of elementary matrices.

asked Jan 23, 2019 at 13:12

## $af'(\xi)+bf'(\eta)=0$ for some $0<\xi<\eta<1$

asked Mar 24, 2019 at 11:41

## Find the maximal value for $\left| \int_{0}^{1}(f(x))^2-f(x)dx \right| .$

asked Sep 23, 2018 at 9:03