Problem 517

Erdős Problem #517: declared status 'open'. Formalized: yes. Let $f(z)=\sum_{k=1}^\infty a_kz^{n_k}$ be an entire function (with $a_k\neq 0$ for all $k\geq 1$). Is it true that if $n_k/k\to \infty$ then $f(z)$ assumes every value infinitely often? Prize: no. Tags: analysis.