The Power of q pp 257-287 | Cite as

Partitions into Four Squares

  • Michael D. HirschhornEmail author
Part of the Developments in Mathematics book series (DEVM, volume 49)


Every number is the sum of four squares. But how many partitions into four squares does a number have? This question was posed by D.H. Lehmer, and an answer is found. It is also proved, amongst other things, that the number of partitions into four squares of a number of the form \(72n+69\) is even. Considerable effort is expended to find the generating function of the \(p(72n + 69)\) in a form which exhibits this evenness.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia

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