Is it true that $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$, where $n$ runs over the integers?
The existence of the limes inferior follows from Dirichlet's approximation theorem, but the problem is to prove that it is $0$.
Is it true that $\varliminf_{n \rightarrow +\infty} |n \sin n| = 0$, where $n$ runs over the integers?
The existence of the limes inferior follows from Dirichlet's approximation theorem, but the problem is to prove that it is $0$.
This is an open question. See the comments for more details.