Question

If $p$ is a prime number and $p$ divides $a^2$, then $p$ divides $a$, if $a$ is a ...............

• A. irrational
• B. consecutive to $p$
• C. both $A$ and $B$
• D. positive integer

Answer 1

Answer: (D)

positive integer

Let us consider $p=5,a=25$
$p$ divides $a^2=\frac{a^2}{p}=\frac{625}{5}=125$
$p$ divides $a,\frac{a}{p}=\frac{25}{5}=25$
So, $a$ is a positive integer.

From the given options, only $A$ fits our choice.
Therefore, $A$ is the correct answer.