Newbetuts

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

Convergence of $\sum_{n=0}^{\infty}\sin(x\pi n!)$

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

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

Why does $29^2 : 31^2 : 41^2$ have a close integer approximation with small numbers?

What is the sum of the squares of the differences of consecutive element of a Farey Sequence

Can every algebraic integer of degree $3$ be approximated by a quotient of linearly recurrent integer sequences of degree $3$?

Accumulation points of $ \{x_n \in \mathbb{R}, n \in \mathbb{N} \ \ | \ x_n = n\sin(n) \}$? [duplicate]

When is a sequence $(x_n) \subset [0,1]$ dense in $[0,1]$?

Egyptian fraction series for $\frac{99}{70}-\sqrt{2}$

Is there a 'far' irrational number?

Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$

Drawing approximated regular shapes on square grid

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

Does $ \sqrt[n]{\left\lvert \sin(2^n) \right\rvert} $ have a limit?

New posts in diophantine-approximation

Asymptotic quality of rational approximations to $\pi$

Approximation of a real number via a fraction of coprimes.

Line through the origin mod $1$ visits every sub-cube in $\mathbb{R}^n$.

Effective equidistribution

355/113 and small odd cubes

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

Convergence of $\sum_{n=0}^{\infty}\sin(x\pi n!)$

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

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

Why does $29^2 : 31^2 : 41^2$ have a close integer approximation with small numbers?

What is the sum of the squares of the differences of consecutive element of a Farey Sequence

Can every algebraic integer of degree $3$ be approximated by a quotient of linearly recurrent integer sequences of degree $3$?

Accumulation points of $ \{x_n \in \mathbb{R}, n \in \mathbb{N} \ \ | \ x_n = n\sin(n) \}$? [duplicate]

When is a sequence $(x_n) \subset [0,1]$ dense in $[0,1]$?

Egyptian fraction series for $\frac{99}{70}-\sqrt{2}$

Is there a 'far' irrational number?

Calculate $\lim_{n \to \infty} \sqrt[n]{|\sin n|}$

Drawing approximated regular shapes on square grid

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

Does $ \sqrt[n]{\left\lvert \sin(2^n) \right\rvert} $ have a limit?