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Elementary Proofs of Infinitely Many Congruences for 8-Cores

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Abstract

Using a very elementary argument, we prove the congruences\(\begin{gathered} a_8 (81n + 21) \equiv 0(\bmod 2){\text{ and}} \hfill \\ a_8 (81n + 75) \equiv 0(\bmod 2) \hfill \\ \end{gathered} \) where a8(n) is the number of 8-core partitions of n. We also exhibit two infinite families of congruences modulo 2 for 8-cores.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, The University of Tennessee at Martin, 424 Humanities Building, Martin, Tennessee, 38238–5049

    Louis W. Kolitsch

  2. Department of Science and Mathematics, Cedarville College, P.O. Box 601, Cedarville, Ohio, 45314

    James A. Sellers

Authors
  1. Louis W. Kolitsch
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  2. James A. Sellers
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Kolitsch, L.W., Sellers, J.A. Elementary Proofs of Infinitely Many Congruences for 8-Cores. The Ramanujan Journal 3, 221–226 (1999). https://doi.org/10.1023/A:1006953609540

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  • DOI: https://doi.org/10.1023/A:1006953609540

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