More Modular Arithmetic in Five Regular Partitions by Jacobi Triple Product Formula

Aneela ., M. Khalid Mahmood, Daud Ahmad, Shahbaz Ali


In a paper, Calkin et al., Divisibility properties of the 5-regular and 13-regular partition functions, Integers 8 (2008), [#A60], authors have discussed interesting properties for 5-regular partition functions of integers. In the continuation of this paper, we have obtained and conjectured various interesting results. In this note, we use nothing more than Jacobi's triple product identity to obtain results for 5-Regular Partitions that are stronger than those obtained by Calkin and his collaborators. The motivation for this paper is an observation that some generating functions of 5-Regular partitions are congruent to functions related to the Ramanujan's Q-series.

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