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Let be a random completely multiplicative function, where for each prime we independently choose uniformly at random. Is it true that
with probability ?
Source: erdosproblems.com/1144
A full solution has been claimed but not yet accepted. The statement is true.
Claimed: one pending full claim, not accepted. The site labels the problem OPEN (page last edited 2026-01-26); the claim, filed on its proof-claims tab, is recorded here and not adopted: Høystad 2026, registered on 2026-09-06 with a write-up and a Lean 4 repository, which asserts the answer yes and credits GPT 6 Astra, GPT 5.6 Sol Pro and Fable 5. The repository reports its own axiom audit; this corpus has not built or audited the development, and no review or acceptance of the claim is recorded.