Is there an intuitive explanation as to why Galois Fields exist only for a prime powers?
132133
Number of elements of a finite field
76446
Why are cyclic groups of order $p$ (prime) unique up to isomorphism?
68376
How, if at all, does pure mathematics benefit from $2^{74207281}-1$ being prime?
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
120943
Galois field extension and number of intermediate fields
1060
Minimal polynomial of intermediate extensions under Galois extensions.
46254
Why can't the Polynomial Ring be a Field?
29572
Proof that $2^n-1$ does not always generate primes when primes are plugged in for $n$?
10760
Why is the product of all units of a finite field equal to $-1$?
111935
Irreducible but not prime
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
155771
Product of degree of two field extensions of prime degree
129420
Source to learn Galois Theory
153862
A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime.
78561
Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
116916
What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?
47091
How to construct finite fields of any prime power order?