Problem 135Published on Friday, 29th December 2006, 06:00 pm; Solved by 3916; Difficulty rating: 45%
Given the positive integers, x, y, and z, are consecutive terms of an arithmetic progression, the least value of the positive integer, n, for which the equation, x2 − y2 − z2 = n, has exactly two solutions is n = 27:
342 − 272 − 202 = 122 − 92 − 62 = 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?