The following is a generalization of Lemma 6.4. Let P(x) be a polynomial with integer coefficients and let n be an integer. Show that if the congruence P(x)≡n has a solution mod m1 and also a solution mod m2 where m1 and m2 are coprime, then it has a solution mod m1m2. Give an example where this fails without the coprimeness condition.