If P is a prime number greater than 3, find the remainder when P^2 + 13 is divided by 12.  Pick:  A) 6  B) 1  C) 0  D) 2  E) 7

Rationale: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 13 = 36 n ^ 2 + 12 n + 1 + 13 = 36 n ^ 2 + 12 n + 12 + 2 if p = 6 n - 1 , then p ^ 2 + 13 = 36 n ^ 2 - 12 n + 1 + 13 = 36 n ^ 2 - 12 n + 12 + 2 when divided by 12 , it must leave a remainder of 2 . the answer is d ."
Answer: D