Erdős problem 477

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.

Sources

The source's own material, retained exactly.

6 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

477.lean

Retained formal statement4 of 5

There is no such $A$ for the polynomial $f(x) = X^2$ .

This is shown in [Sek59].

FormalConjectures/ErdosProblems/477.leanErdos477.erdos_477.variants.S_sq1 lineExact file

1∀ (A : Set ℤ), ∃ z, ¬∃! a, a ∈ A ×ˢ ((fun x => Polynomial.eval x (Polynomial.X ^ 2)) '' {n | 0 < n}) ∧ z = a.1 + a.2

SolvedStatement only, no proof