BALKAN 2003 Problem 3

Find all functions $f: \mathbb{Q}\to\mathbb{R}$ which fulfill the following conditions:

a) $f(1)+1>0$ ;

b) $f(x+y) -xf(y) -yf(x) = f(x)f(y) -x-y +xy$ , for all $x,y\in\mathbb{Q}$ ;

c) $f(x) = 2f(x+1) +x+2$ , for every $x\in\mathbb{Q}$ .