# Problem 136: Singleton difference ![graphic](img136.gif) 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?