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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6 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

477.lean

Retained formal statement3 of 5

Probably there is no such $A$ for the polynomial $X^k$ for any $k \ge 2$ . This is asked in [Sek59].

FormalConjectures/ErdosProblems/477.leanErdos477.erdos_477.variants.monomial3 linesExact file

1∀ (k : ℕ),2  2 ≤ k →3    ∀ (A : Set ℤ), ∃ z, ¬∃! a, a ∈ A ×ˢ ((fun x => Polynomial.eval x (Polynomial.X ^ k)) '' {n | 0 < n}) ∧ z = a.1 + a.2

OpenStatement only, no proof

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