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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 187-188
doi:10.1155/S0161171294000256

Congruences involving F-partition functions

James Sellers

Department of Science and Mathematics, Cedarville College, Cedarville 45314, OH, USA

Abstract

The primary goal of this note is to prove the congruence ϕ3(3n+2)≡0(mod3), where ϕ3(n) denotes the number of F-partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n), the number of F-partitions of n with 2 colors.