Prove that there is no non-constant polynomial $p(n)$ with integer coefficients that only takes prime values
10514
Proof that no polynomial with integer coefficients can only produce primes
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
131289
Polynomial with a root modulo every prime but not in $\mathbb{Q}$.
78342
When is $\phi(n)$ a prime number?
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
8710
Bounds for $n$-th prime
59261
If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.
104965
Find $n$ such that polynomial is divisible
10266
Minimal polynomial reducible modulo every prime $p$
4885
Polynomials with integer coefficients such that $p(a)=b,p(b)=c,p(c)=a$
155575
Proving a polynomial $f(x)$ composite for infinitely many $x$
134068
When polynomials f(x) and f'(x) are relatively prime, f(x) has no repeated roots. Why?
70463
Let $p$ be prime and $a$ be a natural not divisible by $p$. Then, $\exists$ integers $x,y$ such that $ax\equiv y \pmod{p}$ with $0<|x|,|y|<\sqrt{p}$
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
18302
List the primes for which the following system of linear equations DOES NOT have a solution in $\mathbb{Z}_p$