if p is a prime number greater than 3, find the remainder when p ^ 2 + 16 is divided by 12. Choose the correct choice from the following options:
A) 5
B) 1
C) 0
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">16 + 25</gadget>
<output>41</output>

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

<gadget id="calculator">41 - 36</gadget>
<output>5</output>

<result>A</result>
if p is a prime number greater than 3, find the remainder when p ^ 2 + 16 is divided by 12.
subtract(add(16, power(add(const_1, const_4), const_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 + 16 = 36 n ^ 2 + 12 n + 1 + 16 = 36 n ^ 2 + 12 n + 12 + 5 if p = 6 n - 1 , then p ^ 2 + 16 = 36 n ^ 2 - 12 n + 1 + 16 = 36 n ^ 2 - 12 n + 12 + 5 when divided by 12 , it must leave a remainder of 5 . the answer is a .