Prove that if $p$ is prime, then an element of $\mathbb{Z} /p \mathbb{Z}$ has at most two square roots.
130300
Proof that every quadratic residue has two roots, modulo a prime
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
42875
The prime elements of the ring $ \mathbb{Z} \! \left[ \dfrac{i \sqrt{3} - 1}{2} \right] $.
7899
Show that if $p$ is prime then $\Bbb Z_p$ is a field
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
33645
Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$.
37947
Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$.
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
18053
Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
127816
Number theory proof mod p
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
126471
At least one prime between $\sqrt{n}$ and $n$?
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.