Cohen's 22 Conjectures on Cyclic Numbers

22 conjectures of Cohen about cyclic numbers (integers with $\gcd(n, \varphi(n)) = 1$ ) settled at once - 16 proved, 6 disproved - together with a complete resolution of a related OEIS problem on sequences whose running averages are Fibonacci numbers (Fried's Conjecture 2).

Result: Proved
Status: Retracted
AI contribution: AI-assisted
Method: Argument
Field: Elementary number theory
Posed by: Cohen (OEIS conjectures); Fried
Year posed: —
Years open: —
Solved: 2025-09-30
Model: GPT-5
Vendor: OpenAI
Collaborators: Duc Hieu Le
Verification: Unreviewed
Publication: Preprint
Significance: 6 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

"All proofs in the paper were assisted by GPT-5" - a blanket credit across 22 resolutions, with no individual attribution, so the lower tier applies.

Verification

Paper has been retracted from arXiv

Source

PaperarXiv

Cohen's 22 Conjectures on Cyclic Numbers

What the AI did

Verification

Source

Discussion3