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a! b! = a! + b! + c! , factorial diophantine

Source: Switzerland 2020 Swiss MO p5

December 30, 2022
Diophantine equationfactorialnumber theorydiophantineBritishMathematicalOlympiad

Problem Statement

Find all the positive integers a,b,ca, b, c such that a!ā‹…b!=a!+b!+c!a! \cdot b! = a! + b! + c!
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