Proof of a conjecture by Ahlgren and Ono on the non-existence of certain partition congruences

摘要

Let p(n) denote the number of partitions of n. Let A, B G N with A > B and ￡ ≥ 5 a prime, such that. Then we will prove that ￡|A and. This settles an open problem by Scott Ahlgren and Ken Ono. Our proof is based on results by Deligne and Rapoport.