Problem Statement
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?
Categories:
Diophantine Approximation Number Theory
Progress
The infamous Littlewood conjecture.Source: erdosproblems.com/495 | Last verified: January 15, 2026