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Problem 233


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?