Let \(P(x),Q(x)\) be monic polynomials with integer coeeficients. Let \(a_n=n!+n\) for all natural numbers \(n\). Show that if \(\frac{P(a_n)}{Q(a_n)}\) is an integer for all positive integer \(n\) then \(\frac{P(n)}{Q(n)}\) is an integer for every integer \(n\neq0\).