Abstract
In the present work, we discover some new congruences modulo 5 for \(p_r(n)\), the general partition function by restricting r to some sequence of negative integers. Our emphasis throughout this paper is to exhibit the use of q-identities to generate the congruences for \(p_r(n)\).
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ACKNOWLEDGMENT
The authors thank Prof. A. Bayad, Universite d'Evry Val d'Essonne, France, for giving the valuable suggestions during the preparation of this paper.
Funding
The first author thanks SERB, DST, India for sanctioning the project [EMR/2016/001601]. The third author's research is partially supported by the UGC Start-Up Research grant no. F.30-489/2019(BSR).
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 7, pp. 83–88.
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Srivatsa Kumar, B.R., Shruthi & Ranganatha, D. Some New Congruences Modulo 5 for the General Partition Function. Russ Math. 64, 73–78 (2020). https://doi.org/10.3103/S1066369X20070099
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DOI: https://doi.org/10.3103/S1066369X20070099