Problem

Source: Ukraine 2005 grade 11

Tags: function, vector, modular arithmetic, algebra unsolved, algebra



Find all monotone (not necessarily strictly) functions $ f: \mathbb{R}^{+}_0\rightarrow \mathbb{R}$ such that: $ f(x+y)-f(x)-f(y)=f(xy+1)-f(xy)-f(1) \forall x,y \ge 0$; $ f(3)+3f(1)=3f(2)+f(0).$