proving that -1 is square if p = 1 mod 4
120459
Problem with finding the GCD in the Field of Polynomials mod p
67899
Integer squares of the form $x^4+x^3+x^2+x+1$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
83753
Why $\,p \cdot (p^{-1} \mod q) + q \cdot (q^{-1} \mod p) = pq + 1$?
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
64453
Prove if $(a,p)=1$, then $\{a,2a,3a,...,pa\}$ is a complete residue system modulo $p$.
11506
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
115241
If $p$ and $q = 2p + 1$ are both odd primes, show that $-4$ and $2(-1)^{(1/2)(p-1)}$ are both primitive roots modulo $q$.
102234
Show $a^p \equiv a \mod 2p$
103360
Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime
148647
If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$