Further Results for Partitions Into Four Squares of Equal Parity

Michael D.Hirschhorn1, James A.Sellers2
1 School of Mathematics UNSW Sydney 2052 Australia
2Department of Mathematics Penn State University 107 Whitmore Laboratory University Park, PA 16802 USA

Abstract

We prove several results dealing with various counting functions for partitions of an integer into four squares of equal parity. Some are easy consequences of earlier work, but two are new and surprising. That is, we show that the number of partitions of \(72n+ 60\) into four odd squares (distinct or not) is even.