Question 23
N5 (ROM) Let $\mathbb N_0$ denote the set of nonnegative integers. Find a bijective function $f$ from $\mathbb N_0$ into $\mathbb N_0$ such that for all $m,n\in\mathbb N_0$,
$$f(3mn+m+n)=4f(m)f(n)+f(m)+f(n).$$
$$f(3mn+m+n)=4f(m)f(n)+f(m)+f(n).$$