Prove or Disprove: $e = m\pi + n$ for some integers $m$ and $n$.

Question

I would like to prove or disprove the following statement:

There exist integers $m$ and $n$ such that $e = m\pi + n$ (where $e=2.7...$)

Edit: any pointers would be appreciated.

Answer 1

Nobody knows whether $e \pm \pi$ is rational. So it seems most probable that no one knows the answer to your question.