Infinite families of congruences modulo \(3\) and \(9\) for bipartitions with \(3\)-cores

Authors

  • O. X. M. Yao Jiangsu University

Keywords:

bipartitions, $t$-cores, congruences

Abstract

Let \(A3(n)\) denote the number of bipartitions of \(n\) with 3-cores. Recently, Lin [‘Some results on bipartitions with 3-core’, J. Number Theory \(139\) (2014), 44–52] established some congruences modulo 4, 5, 7 and 8 for \(A3(n)\). In this paper, we prove several infinite families of congruences modulo 3 and 9 for \(A3(n)\) by employing two identities due to Ramanujan. DOI: 10.1017/S0004972714000586

Published

2014-11-13

Issue

Vol. 91 No. 1 (2015)

Section

Articles
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