What’s That Doing There?
The integer 8 can be written as the sum of two squares of integers, m2 + n2, in four ways, when (m, n) is (2, 2), (2, -2), (-2, 2), or (-2, -2).
The integer 7 can’t be written at all as the sum of such squares.
Remarkably, over a very large collection of integers from 1 to n, the average number of ways an integer can be written as the sum of two squares approaches π. Why should this be?
