Erdős problem 477 · problems.science

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.

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FormalConjectures/ErdosProblems/

477.lean

Retained formal statement1 of 5

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 $z=a+b$ ?

FormalConjectures/ErdosProblems/477.leanErdos477.erdos_4772 linesExact file

1True ↔2  ∃ f, 2 ≤ f.degree ∧ ∃ A, ∀ (z : ℤ), ∃! ab, ab ∈ A ×ˢ ((fun x => Polynomial.eval x f) '' {n | 0 < n}) ∧ z = ab.1 + ab.2

OpenStatement only, no proof

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