An Unexpected Congruence Modulo 5 for 4--Colored Generalized Frobenius Partitions

In his 1984 AMS Memoir, George Andrews defined the family of k--colored generalized Frobenius partition functions. These are denoted by cϕₖ (n) where k 1 is the number of colors in question. In that Memoir, Andrews proved (among many other things) that, for all n 0, cϕ₂ (5n+3) 05. Soon after, many authors proved congruence properties for various k--colored generalized Frobenius partition functions, typically with a small number of colors. In 2011, Baruah and Sarmah proved a number of congruence properties for cϕ₄, all with moduli which are powers of 4. In this brief note, we add to the collection of congruences for cϕ₄ by proving this function satisfies an unexpected result modulo 5. The proof is elementary, relying on Baruah and Sarmah's results as well as work of Srinivasa Ramanujan.