Problem 136Published on Friday, 29th December 2006, 06:00 pm; Solved by 3367; Difficulty rating: 50%
The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. Given that n is a positive integer, the equation, x2 − y2 − z2 = n, has exactly one solution when n = 20:
132 − 102 − 72 = 20
In fact there are twenty-five values of n below one hundred for which the equation has a unique solution.
How many values of n less than fifty million have exactly one solution?