(a) Prove that the natural number x is prime iff x > 1 and there is no positive integ...

(a) Prove that the natural number x is prime iff x > 1 and there is no positive integer greater than 1 and less than or equal to that divides x.

(b) Prove that if p is a prime number and (Hint: When p is divided by 3, the remainder is either 0, 1, or 2. That is, for some integer