Partitions into Four Squares
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.