Calculatingp(n) Modulo Small Primes Using Quadratic Forms Original Research Article

We use a telescoping method suggested by Ono [5] to computep(n) (mod ℓ) as a weighted sum over ℓ-affine partitions of sizen. When ℓ=2, 3, 5, 7, and 11, these sums are neatly described using binary quadratic forms. Moreover, one immediately obtains classical proofs of the Ramanujan congruences (mod 5), 7, and 11.