Problem 495

Erdős Problem #495: declared status 'open'. Formalized: yes. Let $\alpha,\beta \in \mathbb{R}$. Is it true that$$\liminf_{n\to \infty} n \| n\alpha \| \| n\beta\| =0$$where $\|x\|$ is the distance from $x$ to the nearest integer? Prize: no. Tags: diophantine approximation, number theory.