# Congruence properties for the partition function

@article{Ahlgren2001CongruencePF,
title={Congruence properties for the partition function},
author={Scott Ahlgren and Ken Ono},
journal={Proceedings of the National Academy of Sciences of the United States of America},
year={2001},
volume={98},
pages={12882 - 12884}
}
• Published 23 October 2001
• Mathematics
• Proceedings of the National Academy of Sciences of the United States of America
Eighty years ago, Ramanujan conjectured and proved some striking congruences for the partition function modulo powers of 5, 7, and 11. Until recently, only a handful of further such congruences were known. Here we report that such congruences are much more widespread than was previously known, and we describe the theoretical framework that appears to explain every known Ramanujan-type congruence.
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