Erdős Problem #254

Erdős problem #254 · erdosproblems.com/254

If $A \subseteq \mathbb{N}$ has unbounded dyadic-shell counts and $\sum_{n \in A} \|\theta n\| = \infty$ for every $0 < \theta < 1$, must $A$ be complete - is every sufficiently large integer a sum of distinct elements of $A$?

Result

Proved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Complete Sequences

Posed by

—

Year posed

—

Years open

—

Solved

2026-07-13

Model

GPT-5.6 starships (Claude Fable 5 reviewer)

Vendor

OpenAI / Anthropic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article