Re: [math-fun] Number of sums of squares ...

Without loss of generality x >= y, therefore: x^2 - y^2 = n - 2y^2 can be written in the same number of ways, pi on average. The left hand side is a factorization of n - 2y^2: (x+y)(x-y) = n - 2y^2 So there are pi (perhaps trivial) factorizations of n - 2y^2, on average, for all the varying x and y pairs (i.e. not fixed y). Really? On 7/18/18 12:51 , Colin Wright wrote:

I recently saw the following claim:

"On the average, the number of ways of expressing a positive integer n as a sum of two integral squares, x^2 + y^2 = n, is pi"

Can anyone confirm or deny this?

Thanks.

Colin