Question 5
Let $\mathbb Z,\mathbb N_0$ denote the integers and nonnegative integers. Find all increasing functions $f:\mathbb N_0\to\mathbb Z$ satisfying
$$f(2)=7,\qquad f(mn)=f(m)+f(n)+f(m)f(n)\quad(m,n\in\mathbb N_0).$$
$$f(2)=7,\qquad f(mn)=f(m)+f(n)+f(m)f(n)\quad(m,n\in\mathbb N_0).$$