Erdős Problem #477

Erdős problem #477 · erdosproblems.com/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.

Result

Proved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Argument

Field

Additive Number Theory

Posed by

—

Year posed

1980

Years open

46y

Solved

2026-06

Model

GPT-5.5 Pro

Vendor

OpenAI

Collaborators

—

Verification

Unreviewed

Publication

Preprint

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article