Abstract
The partition function p(n) enjoys some remarkable congruence properties. Most notable are the celebrated Ramanujan congruences p(5n+4)≡0 (mod 5), p(7n+5)≡0 (mod 7), and p(11n+6)≡0 (mod 11). After a discussion of the rationale behind these congruences, we discuss generalizations and open questions regarding the behaviour of the partition function.
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Murty, M.R., Murty, V.K. (2013). Arithmetic of the Partition Function. In: The Mathematical Legacy of Srinivasa Ramanujan. Springer, India. https://doi.org/10.1007/978-81-322-0770-2_7
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DOI: https://doi.org/10.1007/978-81-322-0770-2_7
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