Prove that $f(x)=(x^2-2)(x^2-3)(x^2-6)$ has a root in $\mathbb{F}_p$ for every $p$ prime number
121717
Prove that $z^2 \equiv ab\pmod p$ is solvable if and only if both or neither of $x^2 \equiv a \pmod p$, $x^2 \equiv b \pmod p$ are solvable.
145509
Prove the roots of $p(z)+z^n\bar{p}(\frac{1}{z})$ lie on the unit circle
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
131488
Show that $p^3+4$ is prime
148671
Trying to factor $x^4-3$ over $\Bbb{F}_p$ with $p\equiv 3\mod{4}$
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
119657
If $ f _p(x)=1+x+x^2+ \cdots +x^{p-1} $ where $p$ is prime number, $e$ is any positive integer.
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 $\mathbb{Q}$?
84641
Infiniteness of set of primes such $f$ have root $\mod p$
104484
Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
134068
When polynomials f(x) and f'(x) are relatively prime, f(x) has no repeated roots. Why?
118266
If $f^2(b) - f^2(a) = b^2 - a^2$, then the equation $f'(x)f(x) = x$ has at least one root in (a, b).
106401
Prove: $p-mq | f(m)$ where $m$ is any integer