Let b, c be integer numbers, and define f(x)=(x+b)2−c.i) If p is a prime number such that c is divisible by p but not by p2, show that for every integer n, f(n) is not divisible by p2.ii) Let q=2 be a prime divisor of c. If q divides f(n) for some integer n, show that for every integer r there exists an integer n′ such that f(n′) is divisible by qr. algebrapolynomialnumber theory proposednumber theory