a) Use fundamental Theorem of Arithmetic to prove that for no natural number n integer 14n terminate in 0.
b) For any natural number n, let d(n) denote number of positive divisors of n. For instance, d(4) = 3 because 4 has 3 positive divisors: 1,2, and 4.
i) Explain those natural numbers n for which d(n) = 2.
ii) Explain those natural numbers n for which d(n) =3.
c) Consider a, b, and c is integers each relatively prime to another integer n. Prove that product abc is relatively prime to n.
d) Given that p is prime, gcd (a, p2) = p and gcd (b, p3) = p2, determine:
(a) gcd (a+b,p4)