Sunday April 26, 2009
This problem asks you to work with arithmetic sequences.
Given that the positive integers, x, y, and z, are consecutive terms of an arithmetic progression, the least value of the positive integer n, such that the equation x^2 - y^2 - z^2 = n has exactly two solutions, is n = 27:

34^2 - 27^2 - 20^2 = 12^2 - 9^2 - 6^2 = 27

It turns out that n = 1155 is the least value which has exactly ten solutions.

How many values of n less than one million have exactly ten distinct solutions?

The Number Theory Library (NTL) may be useful for mapping out a brute-force solution; however, your final solution should be a bit more elegant, as a brute-force approach would be highly inefficient.

(This problem came from Project Euler).
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