## Same differences

### Problem 135

Published on Friday, 29th December 2006, 06:00 pm; Solved by 3822; 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, *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?