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Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function

Number Theory 2020-08-17 v1

Abstract

For any non-negative integer nn and non-zero integer rr, let pr(n)p_r(n) denote Ramanujan's general partition function. By employing qq-identities, we prove some new Ramanujan-type congruences modulo 5 for pr(n)p_r(n) for r=(5λ+1),(5λ+3),(5λ+4),(25λ+1)r=-(5\lambda+1), -(5\lambda+3), -(5\lambda+4), -(25\lambda+1), (25λ+2)-(25\lambda+2), and any integer λ\lambda.

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Cite

@article{arxiv.2008.06398,
  title  = {Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function},
  author = {Nipen Saikia and Jubaraj Chetry},
  journal= {arXiv preprint arXiv:2008.06398},
  year   = {2020}
}

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6 Pages