If $p$ is a prime number and $p$ divides $a^2$, then which conclusion …

Question

If $p$ is a prime number and $p$ divides $a^2$, then which conclusion must be true?

Accepted Answer

A. $p$ divides $a$

This is a standard theorem based on prime factorisation: if a prime divides $a^2$, then that prime must already occur in the factorisation of $a$. Hence $p$ divides $a$.

Answer

$a$ must be prime

Answer

$a$ must equal $p$

Answer

$p$ divides only even numbers