Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
126808
Is it true that if $f(x)$ has a linear factor over $\mathbb{F}_p$ for every prime $p$, then $f(x)$ is reducible over $\mathbb{Q}$?
101882
Does this polynomial evaluate to prime number whenever $x$ is a natural number?
80907
Primes dividing a polynomial
82262
minimal polynomial of nth root of 2 over $\mathbb Q$
250
An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root?
52530
There exists a prime congruent to $m$ mod $p$
156034
sufficient condition for a polynomial to have roots in $[0,1]$
70523
Proving that $x^4 - 10x^2 + 1$ is not irreducible over $\mathbb{Z}_p$ for any prime $p$.
115758
Remainder of division when $p$ is not prime
84746
elementary proof that infinite primes quadratic residue modulo $p$
151729
Existence of a unique polynomial
16592
Irreducible polynomial which is reducible modulo every prime
155245
root of an odd degree polynomial
117484
Why is $c+q$ still a primitive root modulo $q$?
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
64878
Is this polynomial irreducible in $\mathbb{Q}$?
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$