Let $\mathbb{F}$ be a finite field such that for every $a ∈ \mathbb{F}$ the equation $x^2 =a$ has a solution in $\mathbb{F}$. Then which is true?
1. The characteristic of $\mathbb{F}$ must be $2$
2. $\mathbb{F}$ must have a square number of elements
3. The order of $\mathbb{F}$ is a power of $3$
4. $\mathbb{F}$ must be a field with prime number of elements
Can anyone suggest to me how I can solve this problem?