Proof that if the set $F_p={0, 1, ..., p-1}$ is a field defined with addition and multiplication mod p, then $p$ must be a prime
48405
Why does the characteristic of a finite field always have to be prime?
135586
Prove that the preimage of a prime ideal is also prime.
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
63659
If D is an Integral Domain and has finite characteristic p, prove p is prime.
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
126127
A field extension of prime degree
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
93898
Prove that for any prime p, there is a complete set of mod p residues {q1, . . . , qp}, where each qi is prime.
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
94174
Ring of polynomials over a field has infinitely many primes
16643
A slick proof that a field which is finitely generated as a ring is finite
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
110752
$g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.