Abstract
For primes ℓ we obtain a simple formula for p(N) (mod ℓ) as a weighted sum over ℓ-square affine partitions of N. When ℓ ∈ {3,5,7,11}, the weights are explicit divisor functions. The Ramanujan congruences modulo 5, 7, 11, 25, 49, and 121 follow immediately from these formulae.
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Ono, K. The Residue of p(N) Modulo Small Primes. The Ramanujan Journal 2, 47–54 (1998). https://doi.org/10.1023/A:1009705807315
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DOI: https://doi.org/10.1023/A:1009705807315