Congruences Involving F-Partition Functions

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

Original languageEnglish (US)
Pages (from-to)187-188
Number of pages2
JournalInternational Journal of Mathematics and Mathematical Sciences
Issue number1
StatePublished - 1994
Externally publishedYes


  • Congruence
  • partitions


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