Two congruences involving 4-cores

Michael D. Hirschhorn, James Sellers

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The goal of this paper is to prove two new congruences involving 4-cores using elementary techniques; namely, if a4(n) denotes the number of 4-cores of n, then a4(9n + 2) ≡ 0 (mod 2) and a4(9n + 8) ≡ 0 (mod 4).

Original languageEnglish (US)
Article numberR10
Pages (from-to)1-8
Number of pages8
JournalElectronic Journal of Combinatorics
Issue number2 R
StatePublished - Dec 1 1996
Externally publishedYes


  • Congruence
  • Partitions
  • t-cores


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