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3^x + 4^y = 5^z

Source: IMO ShortList 1991, Problem 17 (HKG 4)

August 15, 2008
modular arithmeticalgebranumber theoryequationIMO Shortlist

Problem Statement

Find all positive integer solutions x,y,z x, y, z of the equation 3^x \plus{} 4^y \equal{} 5^z.
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