International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 6, Pages 333-340
doi:10.1155/S0161171202007342

Computational proofs of congruences for 2-colored Frobenius partitions

Dennis Eichhorn1 and James A. Sellers2

1Department of Mathematics, University of Arizona, Tucson 85721, AZ, USA
2Department of Mathematics, Penn State University, University Park 16802, PA, USA

Received 13 April 2001

Copyright © 2002 Dennis Eichhorn and James A. Sellers. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.