number-theory / Additive Number Theory

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.

10Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Append-only history

Frontier timeline

number-theoryJun 1, 2026Significance 10/100Registry: unreviewed

Erdős Problem #477

Prior state unknownproved

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.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Source authenticated

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.

Recorded attempts

Evidence graph

Connected research record

No public relationships recorded yet.