How to show that there are infinitely many prime numbers $p$ such that the polynomial f has a zero in $\mathbb Z_p$?
80907
Primes dividing a polynomial
1702
Proving that there are infinitely many primes with remainder of 2 when divided by 3
136310
Prime number in a polynomial expression
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
36819
Show there are infinitely many primes that are equivalent to 1 mod 8.
6722
to show $f$ is a polynomial in $z$
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
95594
Prove that a polynomial is irreducible or the field contains a $p$th root
252
Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
141418
When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
85681
Cardinality of polynomials with real coefficients
131971
If $k>0$ is a positive integer and $p$ is any prime, when is $\mathbb Z_p[\sqrt{k}] =\{a + b\sqrt k~|~a,b \in\mathbb Z_p\}$ a field.
5142
Infinitely many primes of the form $pn+1$