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1 /k ! + 1 /l ! + 1 /m ! = 1 / n !

Source: 2011 Swedish Mathematical Competition p1

April 30, 2021
number theoryDiophantine equationdiophantine

Problem Statement

Determine all positive integers kk, ℓ\ell, mm and nn, such that 1k!+1ℓ!+1m!=1n!\frac{1}{k!}+\frac{1}{\ell!}+\frac{1}{m!} =\frac{1}{n!}
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