Problem 477

Erdős Problem #477: declared status 'open'. Formalized: yes. Is there a polynomial $f:\mathbb{Z}\to \mathbb{Z}$ of degree at least $2$ and a set $A\subset \mathbb{Z}$ such that for any $n\in \mathbb{Z}$ there is exactly one $a\in A$ and $b\in \{ f(n) : n\in\mathbb{Z}\}$ such that $n=a+b$? Prize: no. Tags: number theory.