Question 30
Find all functions $f : \mathbb{Z} \to \mathbb{Z}$ satisfying:
(1) For any positive integer $M$, there exists an integer $k$ with $|f(k)| \ge M$;
(2) For any integers $m, n$,
$$2f(m)f(n) - f(m - n) - 1$$ is a perfect square.
(1) For any positive integer $M$, there exists an integer $k$ with $|f(k)| \ge M$;
(2) For any integers $m, n$,
$$2f(m)f(n) - f(m - n) - 1$$ is a perfect square.