A reformulation of Ramanujanʹs partition congruences

The Ramanujan partition congruences concern p(nδ + λ), where δ = 5α7β11γ, 24λ ≡ 1 (mod δ) and 0 < λ < δ. We give an explicit expression for λ in terms of δ and a new formulation of the partition congruences.