if p is a prime number greater than 3, find the remainder when p ^ 2 + 14 is divided by 12. Choose the correct choice:  A) 6  B) 1  C) 3  D) 8  E) 7
<gadget id="calculator">1 + 4</gadget>
<output>5</output>

<gadget id="calculator">5 ** 2</gadget>
<output>25</output>

<gadget id="calculator">14 + 25</gadget>
<output>39</output>

<gadget id="calculator">12 * 3</gadget>
<output>36</output>

<gadget id="calculator">39 - 36</gadget>
<output>3</output>

<result>C</result>
if p is a prime number greater than 3, find the remainder when p ^ 2 + 14 is divided by 12.
subtract(add(14, power(add(const_1, const_4), 2)), multiply(12, 3))
"every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 14 = 36 n ^ 2 + 12 n + 1 + 14 = 36 n ^ 2 + 12 n + 12 + 3 if p = 6 n - 1 , then p ^ 2 + 14 = 36 n ^ 2 - 12 n + 1 + 14 = 36 n ^ 2 - 12 n + 12 + 3 when divided by 12 , it must leave a remainder of 3 . the answer is c ."