Problem 233
Lattice points on a circle
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 ?
圆周上的格点
作过点(0,0)、(N,0)、(0,N)和(N,N)的圆，记圆周上坐标为整数的点的数目为f(N)。
可以看出f(10000) = 36。
有些正整数N ≤ 1011且f(N) = 420，这些正整数的和是多少？