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Classic Diophantine Equation

Source: 2021 ISL N5

July 12, 2022
number theoryAZE IMO TST

Problem Statement

Show that n!=an−1+bn−1+cn−1n!=a^{n-1}+b^{n-1}+c^{n-1} has only finitely many solutions in positive integers.
Proposed by Dorlir Ahmeti, Albania
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