On congruence properties of p(n, m).

摘要

Though congruence properties of p( n) modulo an odd prime ℓ have been well studied since the time of Ramanujan, congruence properties of p(n, m) modulo ℓ were unknown beyond m = 3. The purpose of this thesis is to detail the discovery and proofs of several infinite families of congruence properties of p(n, m) modulo every odd prime ℓ. We will also prove a striking congruence relationship of the form p(n, m) ≡ p( n', m) (mod ℓ).