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INFINITE FAMILIES OF CONGRUENCES MODULO 3 AND 9 FOR BIPARTITIONS WITH 3-CORES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 1 / February 2015
- Published online by Cambridge University Press:
- 27 August 2014, pp. 47-52
- Print publication:
- February 2015
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- Article
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Let
$A_{3}(n)$ denote the number of bipartitions of 
$n$ with 3-cores. Recently, Lin [‘Some results on bipartitions with 3-core’, J. Number Theory139 (2014), 44–52] established some congruences modulo 4, 5, 7 and 8 for 
$A_{3}(n)$. In this paper, we prove several infinite families of congruences modulo 3 and 9 for 
$A_{3}(n)$ by employing two identities due to Ramanujan.
