International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 187-188
Congruences involving -partition functions
Department of Science and Mathematics, Cedarville College, Cedarville 45314, OH, USA
Received 10 August 1992
Copyright © 1994 James 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.
The primary goal of this note is to prove the congruence , where denotes the number of -partitions of with at most repetitions. Secondarily, we conjecture a new family of congruences involving , the number of -partitions of with colors.