Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915735118282752 |
|---|---|
| author | Alexeev, Boris Mixon, Dustin G. |
| author_facet | Alexeev, Boris Mixon, Dustin G. |
| contents | We resolve a $1000 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 "favourite" 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 discovered 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 code a Lean proof of both Hall's and our counterexamples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof Alexeev, Boris Mixon, Dustin G. Combinatorics Number Theory We resolve a $1000 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 "favourite" 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 discovered 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 code a Lean proof of both Hall's and our counterexamples. |
| title | Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2510.19804 |