Show that if F is a finite field, then $F^F=P_F$.
62615
If F is a finite field, then $F^F=P_F$.
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
102553
How to show that $f(z) = f(i)$
151018
Proving that any finite integral domain is a field.
46795
Explicit construction of a finite field with $p^n$ elements
745
$F(x)$ versus $F[x]$ where $F$ is a field
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
23712
$F$ is a finite field of size $s$. Prove that if $s=2^m$ for some $m>0$, then all elements of F have a square root.
43059
Show that $g^k=e$ if and only if the order of $g$ is finite and divides $k$.
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
48873
Let $K$ be a field and $f(x)\in K[X]$ be a polynomial of degree $n$. And let $F$ be its splitting field. Show that $[F:K]$ divides $n!$.
73454
Prove that $f$ has finite number of roots
54729
Prove that $f$ has a fixed point .
6722
to show $f$ is a polynomial in $z$
116594
Finite fields are isomorphic
86174
Finding an isomorphism between these two finite fields
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$