## Quadratic Differences

#### Problem

The positive integers, $x$, $y$, and $z$ are consecutive terms in an arithmetic progression. Given that $n$ is also a positive integer, for how many values of $n$ below one-thousand does the equation $x^2 - y^2 - z^2 = n$ have no solutions?

Problem ID: 295 (26 Nov 2006) Difficulty: 4 Star