Question 67
Find all the functions $f: \mathbb{Z} \to \mathbb{N}$ fulfilling the conditions:
i) $f(m+n) = f(m)+f(n)+2mn$, for every integers $m, n$;
ii) $f(f(x))-f(1)$ is a perfect square for each integer $x$.
i) $f(m+n) = f(m)+f(n)+2mn$, for every integers $m, n$;
ii) $f(f(x))-f(1)$ is a perfect square for each integer $x$.