OPEN
Is it true that, for any $a\in\mathbb{Z}$, there are infinitely many $n$ such that
\[\phi(n) \mid n+a?\]
A conjecture of Graham. Lehmer has conjectured that $\phi(n)\mid n-1$ if and only if $n$ is prime. It is an easy exercise to show that $\phi(n) \mid n$ if and only if $n=2^a3^b$.
