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The Ramanujan Journal

, Volume 8, Issue 3, pp 279–287 | Cite as

On a Problem of Lehmer on Partitions into Squares

  • Michael D. Hirschhorn
  • James A. Sellers
Article

Abstract

In 1948, D.H.Lehmer published a brief work discussing the difference between representations of the integer n as a sum of squares and partitions of n into square summands. In this article, we return to this topic and consider four partition functions involving square parts and prove various arithmetic properties of these functions. These results provide a natural extension to the work of Lehmer.

partitions into squares 

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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • Michael D. Hirschhorn
    • 1
  • James A. Sellers
    • 1
  1. 1.School of MathematicsUNSWSydneyAustralia

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