Year: 2026
Type: preprint
Abstract: Choi, Erdős and Szemerédi showed that there exists an absolute constant $C$ such that for all subsets $A \subseteq \{1, 2, \ldots, 2n\}$ with at least $n+C$ elements, there exist four distinct positive integers whose pairwise sums are all contained in $A$. A proof that one can take $C = 3166$ was recently sketched by the first author, and here we show that we actually have $C = 4$ for all $n \ge 6$, which is optimal. The proof we present was originally conceived of by AI, with the final result proved and formalized by Aristotle, the formal reasoning agent developed by Harmonic.
Source: arXiv (Cornell University)
Authors: van Doorn, Wouter, Erlbacher, John
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215029362