New posts in Diophantine Approximation

Is $22/7$ the closest to $\pi$, among fractions of denominator at most $50$?

Is the sequence $(B_n)_{n \in \Bbb{N}}$ unbounded, where $B_n := \sum_{k=1}^n\mathrm{sgn}(\sin(k))$?

If $m$ and $n$ are integers, show that $\left|\sqrt{3}-\frac{m}{n}\right| \ge \frac{1}{5n^{2}}$

Convergence of $\sum_{n=1}^\infty\frac{\cot \varphi\pi n}{n^s}$

A variant of Kronecker's approximation theorem?

Prove $\sum_{n=1}^\infty\frac{\cot(\pi n\sqrt{61})}{n^3}=-\frac{16793\pi^3}{45660\sqrt{61}}$

Exploiting a Diophantine approximation of $\pi^4$ into giving a series of rationals for $\pi^4$

Lagrange spectrum in diophantine approximation theory

M and n are positive integers such that $2^n - 3^m > 0$. Prove (or disprove) that $2^n - 3^m \geqslant 2^{n-m}-1$.

Prove the inequality $\left|\frac{m}{n}-\frac{1+\sqrt{5}}{2}\right|<\frac{1}{mn}$