Abstract
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.
The original version of this chapter has been revised. The erratum to this chapter is available at https://doi.org/10.1007/978-3-319-57762-3_44.
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Hirschhorn, M.D. (2017). Partitions into Four Squares. In: The Power of q. Developments in Mathematics, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-57762-3_30
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DOI: https://doi.org/10.1007/978-3-319-57762-3_30
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