Problem 136 of Project Euler can be solved in a very easy way, and a very fast way. So lets look at the problem and dive right into the problem which reads

The positive integers,x,y, andz, are consecutive terms of an arithmetic progression. Given thatnis a positive integer, the equation,x^{2}–y^{2}–z^{2}=n, has exactly one solution whenn= 20:

13^{2}– 10^{2}– 7^{2}= 20

In fact there are twenty-five values ofnbelow one hundred for which the equation has a unique solution.

How many values ofnless than fifty million have exactly one solution?

So this sounds a bit like Problem 135? Well it is a lot like that, and this is where we will get out easy solution from. Continue reading →