Computational proofs of congruences for 2-colored Frobenius partitions
Dennis Eichhorn1and James A. Sellers2
Received13 Apr 2001
Abstract
In 1994, the following infinite family of congruences was
conjectured for the partition function cΦ2(n) which counts the number of 2-colored Frobenius partitions of n: for all n≥0 and α≥1, cΦ2(5αn+λα)≡0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α.
In this paper, the first four cases of this family are proved.