Does there exist an integer polynomial $f$ of degree at least two and a set $A \subseteq \mathbb{Z}$ such that every integer has a unique representation $n = a + f(k)$? A manuscript claims the thirteenth powers admit a tiling complement.

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 $z\in \mathbb{Z}$ there is exactly one $a\in A$ and $b\in \{ f(n) : n\in\mathbb{Z}\}$ such that $z=a+b$?