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1/f(n)+1/f(m)=4/(f(n) + f(m)), injective f => m=n

Source: Canada Repêchage 2019/1 CMOQR

March 1, 2020
functioninjective functionInjectivealgebrafunctional equationalgebra solved

Problem Statement

A function ff is called injective if when f(n)=f(m)f(n) = f(m), then n=mn = m. Suppose that ff is injective and 1f(n)+1f(m)=4f(n)+f(m)\frac{1}{f(n)}+\frac{1}{f(m)}=\frac{4}{f(n) + f(m)}. Prove m=nm = n
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