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, 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?
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 →