10. Let de N and 40, 41,..., Ad E Z. Define f(x) = afz + ... + air + 20 Z[X] and for a prime p put fp(t) = [aa]2 + ... + [11]2+ [20] Zp [2]. Prove or disprove each of the following. (a) If f(x) has a rational root with ged(a, b) = 1, then for any prime p there exists (de Z such that fp([c]) = [0]. (b) If f(x) has a rational root with ged(a, b) = 1, then for any prime p such that pb there exists (c) Zsuch that fp([c) = [0]. Hint: You can use it as a fact that if f(x) Z[x], (bx - a) f(x) and ged(a,b) = 1, then f(x)/(b a) has integer coefficients. This fact is a direct consequence of so-called Gauss' Lemma. I couldn't find a simple way of proving this statement, but maybe you can