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` 10^{11} such that `f`(`N`) = 420 ?

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These problems are part of
Project Euler
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