Every irreducible polynomial over $\mathbb F_p$ has a root in $\mathbb F_{p^{\deg f}}$
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
12166
How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
25290
Determine the number of irreducible monic polynomials of degree 3 in $\mathbb F_p[x]$
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
46821
Finding roots in $\mathbb{Z}_p$
156671
Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
78540
Every irreducible polynomial f over perfect field F is separable
36087
Every Function in a Finite Field is a Polynomial Function
60816
Irreducibility of special cyclotomic polynomial.
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
70249
Irreducibility of Polynomials in $k[x,y]$
115299
Elements of $\mathbb{F}_p$ having cube roots in $\mathbb{F}_p$
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$