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a! + b! = 2^{c!}

Source: 2023 Austrian Mathematical Olympiad, Junior Regional Competition , Problem 4

March 26, 2024
number theoryDiophantine equationdiophantine

Problem Statement

Determine all triples (a,b,c)(a, b, c) of positive integers such that a!+b!=2c!.a! + b! = 2^{c!}.
(Walther Janous)
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