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f(m ) - f(n) = (m - n)(g(m) + g(n))

Source: 2010 Saudi Arabia IMO TST I p2

December 27, 2021
functional equationfunctionalalgebra

Problem Statement

Find all functions f,g:N→Nf,g : N \to N such that for all m,n∈Nm ,n \in N the following relation holds: f(m)−f(n)=(m−n)(g(m)+g(n))f(m ) - f(n) = (m - n)(g(m) + g(n)). Note: N={0,1,2,...}N = \{0,1,2,...\}
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