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Diophantine equation with factorial

Source: 2022 Junior Macedonian Mathematical Olympiad P1

June 7, 2022
number theoryDiophantine equationfactorial

Problem Statement

Determine all positive integers aa, bb and cc which satisfy the equation a2+b2+1=c!.a^2+b^2+1=c!.
Proposed by Nikola Velov
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