Find all functions $f,g : N \to N$ such that for all $m ,n \in N$ the following relation holds: $$f(m ) - f(n) = (m - n)(g(m) + g(n))$$. Note: $N = \{0,1,2,...\}$
Source: 2010 Saudi Arabia IMO TST I p2
Tags: functional equation, functional, algebra
Find all functions $f,g : N \to N$ such that for all $m ,n \in N$ the following relation holds: $$f(m ) - f(n) = (m - n)(g(m) + g(n))$$. Note: $N = \{0,1,2,...\}$