if p is a prime number greater than 3 , find the remainder when p ^ 2 + 15 is divided by 12 .
"every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 15 = 36 n ^ 2 + 12 n + 1 + 15 = 36 n ^ 2 + 12 n + 12 + 4 if p = 6 n - 1 , then p ^ 2 + 15 = 36 n ^ 2 - 12 n + 1 + 15 = 36 n ^ 2 - 12 n + 12 + 4 when divided by 12 , it must leave a remainder of 4 . the answer is b ."
subtract(add(15, power(add(const_1, const_4), 2)), multiply(12, 3))