Short proofs in combinatorics and number theory

2026/03/31 by Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2 · 1 voice
#math.CO #math.NT

paper · pdf

Abstract

We give a triplet of short proofs, each of which answers a question raised by Erdős. The first concerns the small prime factors of \binomnk, the second concerns whether an additive basis A can always be split into pieces A₁ and A₂ such that each of A_i + A_i has bounded gaps, and the final concerns whether \αp\ is "well-distributed" in the sense introduced by Hlawka and Petersen. In each case, the proof is due entirely to an internal model at OpenAI.

Citations

• Dense clusters of primes in subsets

Discussions

• Two more Erdos problems automatically solved arxiv.org/pdf/2603.29961 [bsky, 67 points, 2 comments]

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