How Many Positive Integer Triples (x, y, z) Satisfy xyz = 72? | Olympiad Number Theory Challenge

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Find, with proof, all triples (x, y, z) of positive integers such that 2018^x=y^2+z^2+1. Find, with proof, all triples (x, y, z) of positive integers such that 2018^x=y^2+z^2+1.
A beautiful international math olympiad problem A beautiful international math olympiad problem
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