On a Problem of Lehmer on Partitions into Squares |
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Authors: | Michael D Hirschhorn James A Sellers |
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Institution: | (1) School of Mathematics, UNSW, Sydney, 2052, NSW, Australia;(2) Department of Mathematics, Penn State University, 107 Whitmore Laboratory, University Park, PA 16802, USA |
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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. |
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Keywords: | partitions into squares |
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