Erdős Problem #123

Erdős problem #123 · erdosproblems.com/123

Let $a,b,c>1$ be pairwise coprime integers. Is every large integer a sum of distinct numbers of the form $a^k b^l c^m$ ($k,l,m\ge 0$), none dividing another?

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Number Theory

Posed by

Paul Erdős, Mordechai Lewin

Year posed

1996

Years open

30y

Solved

2026-07

Model

GPT-5.6

Vendor

OpenAI

Collaborators

Colin Snyder

Verification

Lean-verified

Publication

Announced

Significance

11 / 100*

Disclosed cost

—

Wikipedia

No dedicated article