# Problem 233: Lattice points on a circle

![graphic](img233.gif)

Let f(N) be the number of points with integer coordinates that are on a
circle passing through (0,0), (N,0),(0,N), and (N,N). It can be shown
that f(10000) = 36. What is the sum of all positive integers N ≤ 1011
such that f(N) = 420 ?