Littlewood conjecture

for any two real numbers \alpha, \beta, \liminf_{n \rightarrow \infty} n\,\Vert n\alpha\Vert\,\Vert n\beta\Vert = 0, where \Vert x\Vert is the distance from x to the nearest integer.

Open the “Diophantine approximation and transcendental number theory” section on Wikipedia →

Source: List of unsolved problems in mathematics (CC BY-SA 4.0)