alleryIf $p$ is a prime number and $p$ divides $a^2$, then which conclusion must be true?
A$p$ divides $a$
B$a$ must be prime
C$a$ must equal $p$
D$p$ divides only even numbers
Answer & Solution
Correct 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 $a$.**
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