alleryIf $p$ is a prime number and $p$ divides $a^2$, then which statement must be true?
A$p$ divides $a$
B$a$ must be prime
C$a$ must be even
D$p$ divides $a+1$
Answer & Solution
Correct answer: A. $p$ divides $a$
A standard number theory result says that if a prime $p$ divides $a^2$, then $p$ must divide $a$.
This follows from the prime factorisation property of integers.
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