Erdős Problem 479

Reference: erdosproblems.com/479

theorem erdos_479 : (∀ k > 1, {n : ℕ | 2 ^ n ≡ k [MOD n]}.Infinite) ↔ sorry

Is it true that, for all $k\neq 1$, there are infinitely many $n$ such that $2^n\equiv k\pmod{n}$?