Inverse Pythagorean Triple

\[ \left ( \dfrac1x \right)^2 + \left ( \dfrac1y \right)^2 = \left ( \dfrac1z \right)^2 \] For all triples of natural numbers \((x, y, z)\) fulfilling the equation above, sum all the distinct values of \(z\) less than 100.


Inspired from this discussion about Inverse Pythagorean Theorem.

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