Bibliographic Details
| Title: |
Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof. |
| Authors: |
Alexeeva, Boris boris.alexeev@gmail.com, Mixon, Dustin G.1 mixon.23@osu.edu |
| Source: |
Proceedings of the National Academy of Sciences of the United States of America. 5/26/2026, Vol. 123 Issue 21, p1-9. 9p. |
| Subjects: |
Difference sets, Formal verification, Language models, Refutation (Logic), ChatGPT |
| Abstract: |
We resolve a $1,000 Erdős prize problem, complete with formal verification generated by a large language model. In over a dozen papers, beginning in 1976 and spanning two decades, Paul Erdős repeatedly posed one of his "favorite" conjectures: every finite Sidon set can be extended to a finite perfect difference set. We establish that {1, 2, 4, 8, 13} is a counterexample to this conjecture. During the preparation of this paper, we found that although this problem was presumed to be open for half a century, Marshall Hall, Jr. published a different counterexample three decades before Erdős first posed the problem. With a healthy skepticism of this apparent oversight, and out of an abundance of caution, we used ChatGPT to vibe prove both Hall’s and our counterexamples in Lean. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
