A polynomial with a root in $\mathbb{F}_p \ \forall p$, where $p$ is prime, but no root in $\mathbb{Z}$
131289
Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
18336
$x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
38419
Existence of Polynomial with whom product contains only prime powers
84641
Infiniteness of set of primes such $f$ have root $\mod p$
154507
If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
94682
Polynomial: prove there is no double root
80188
There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
121404
How to factor polynomials in $\mathbb{Z}_n$?
64878
Is this polynomial irreducible in $\mathbb{Q}$?
18053
Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
92537
Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots
156034
sufficient condition for a polynomial to have roots in $[0,1]$
19230
Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
108896
Prime ideal in a polynomial ring over an integrally closed domain
40014
A polynomial that is zero on an open set
124380
existence of sequence of polynomial