Problem 135Published on Friday, 29th December 2006, 06:00 pm; Solved by 2901
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?