How to prove that one of $2,3,6$ is a square modulo every prime $p$?
87468
When is 6 a square in Zp
34588
Number Theory: $p!+p=n^2$, $p$ = prime
68635
When is $2$ a quadratic residue mod $p$?
29640
If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
32803
Prove that if b is coprime to 6 then $b^2 \equiv 1 $ (mod 24)
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
17660
Show that the odd prime divisors of $n^2+n+1$ are of form $6k+1$ (exclude 3)
138941
If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p.
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
67332
Sum of two squares modulo p
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
130300
Proof that every quadratic residue has two roots, modulo a prime
146512
Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers