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(m^2 + 20mn + n^2(/(m^3 + n^3) pos. integer when m,n coprime pos. integers

Source: KJMO 2006 p5

May 1, 2019

number theorycoprimepositive integersIntegers

Problem Statement

Find all positive integers that can be written in the following way

\frac{m^2 + 20mn + n^2}{m^3 + n^3}

Also,

m,n

are relatively prime positive integers.