GPT 5.2 helps solve Erdős problem #728 (www.erdosproblems.com)

Researchers have utilized GPT-5.2 to make advancements in resolving Erdős problem #728, a mathematical inquiry that examines the conditions under which certain binomial coefficients can be integers. While the problem has been vaguely stated in previous literature, recent work inspired by computational exploration has reformulated the question more clearly. The focus now is on the relationship between the variables \(a\), \(b\), and \(n\), specifically questioning whether the divisibility condition \(a!b! \mid n!(a+b-n)!\) implies \(a+b \leq n + O(\log n)\). This development is significant for the AI/ML community as it showcases the potential of large language models, like GPT-5.2, to contribute to complex mathematical research. The model's ability to parse ambiguities and propose precise formulations indicates a valuable intersection between AI and theoretical mathematics. The exploration surrounding the Erdős problem highlights the capability of AI tools to assist in generating mathematical insights and reframing questions that may drive further exploration in combinatorics and beyond.