Erdős problem 123 · problems.science

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?

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No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/123.lean

Formal Conjectures

FormalConjectures/ErdosProblems/123.leanErdos123.erdos_1236 linesExact file

1True ↔2  ∀ a > 1,3    ∀ b > 1,4      ∀ c > 1,5        Erdos123.PairwiseCoprime a b c →6          Erdos123.IsDComplete (↑(Submonoid.powers a) * ↑(Submonoid.powers b) * ↑(Submonoid.powers c))

SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

Jayyhk Erdős Leanjayyhk:erdos:123
PLBY Lean proofsErdosProblems.Erdos123

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

argument
VibeMathed
Machine
GPT-5.6
People
Colin Snyder
Reported outcome
resolved
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