The 2014 Problem is such a Failure. Let's Try 2015

Because next year is \(2015\), find the number of ordered triples \((x, y, z)\) where \(x\), \(y\), and \(z\) are positive integers such that \(x \leq y \leq z\) that will satisfy the equation:

\(x ^2 + y^2 + z^2 = 2015\)

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