Possible sizes of finite fields and the relation to the characteristic of the field
3703
Order of finite fields is $p^n$
113175
Why is the algebraic closure of a finite field countable?
103561
Residue fields of schemes of finite type (over $\mathbb{Z}$)
57084
Characteristic of the following field?
121823
Number of subrings of a Field
155569
Choosing finite field size in Shamir's Secret Sharing Scheme
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
143321
Number of roots of a polynomial over a finite field
115449
Inclusion of Fields whose order is a prime power
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
130720
Special linear algebra over finite field with characteristic 3
36034
Degree of splitting field less than n!
146617
A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
78350
When does a finite ring become a finite field?
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.
139499
The algebraic closure of a finite field and its Galois group