I shall be highly glad if anyone can help me to solve these two problems on finite fields. I am writing in the same post as they are related to the same topic.
- Let $\mathbb{F}$ be a finite field such that $x^2=a$ has a solution in it for every $a\in\mathbb{F}$. Then
a) It is of characteristic 2
b) It must have a square number of elements.
c) Its order is power of 3
d) Its order is a prime number.- If $|\mathbb{F}|=5^{12}$, then what is the total number of subfields of this field?
a) 3
b) 5
c) 8
d) 6