e-mail: lovejoy@math.psu.edu

**Extension of Ramanujan's Congruences for the
Partition Function Modulo Powers of 5**

**Abstract**

We investigate the optimality of Ramanujan's congruences for the partition
function modulo powers of 5. In particular, are there subprogressions
of Ramanujan's arithmetic progressions, other than those found by Ramanujan
himself, where the congruence modulo 5^j is actually a congruence modulo
a higher power of 5? We answer this question in the affirmative byeplicitly
exhibiting infinitely many such systematic extensions.