The solvability in field of Prime Characteristic p
10548
The equation $-1 = x^2 + y^2$ in finite fields
85915
Principal prime ideals are minimal among prime ideals in a UFD
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
23153
$\bmod p\!:\ x^2\equiv 1\iff x\equiv \pm1\ $ for prime $p$
31064
Showing $x^8\equiv 16 \pmod{p}$ is solvable for all primes $p$
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
146591
Inseparable polynomial over a non-perfect field
62603
Characterizations of the $p$-Prüfer group
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
111347
Finding an example of field extensions satisfying certain properties
121301
What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
103552
The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
86626
Finite fields, existence of field of order $p^n$,proof help
3037
Integral domain without unity has prime characteristic?
155771
Product of degree of two field extensions of prime degree
117132
Rationals of the form $\frac{p}{q}$ where $p,q$ are primes in $[a,b]$