Erdős Problem #707: Sidon Sets and Perfect Difference Sets
resolvedconfidence 70%
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Erdős conjectured, in over a dozen papers spanning 1976 to 1997 and with a 1000 dollars prize attached, that every finite Sidon set extends to a perfect difference set modulo $p^2+p+1$ for some prime $p$. Alexeev and Mixon establish that $\{1,2,4,8\}$ is a counterexample - and discovered along the way that Marshall Hall, Jr. had published a different counterexample three decades before Erdős first posed the problem, unnoticed by the community for half a century.
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fidelity, correctness, priority, or novelty.
What AI did
ChatGPT (GPT-5)
The mathematics is the humans'; the paper is candid that LLMs failed at the two things they are usually praised for here - they never located Hall's paywalled prior solution, and "even after we knew what exactly to prove, it couldn't help us close the gap." What ChatGPT did do: write the complete Lean formalization of both counterexamples ("we decided to vibe code the whole proof... about a week... somehow it succeeded"). Earlier versions of the paper listed ChatGPT and Lean as authors until arXiv policy required their removal.
Both Hall's and the new counterexample are formalized and kernel-checked in Lean, with the formalization written by ChatGPT and audited by the authors; erdosproblems.com marks the problem disproved with the proof verified in Lean.