Quadratic residue p-1 modulo p for p primes
27287
$-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$
104484
Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
140198
Let $a$ be a quadratic residue modulo $p$. Prove that the number $b\equiv a^\frac{p+1}{4} \mod p$ has the property that $b^2\equiv a \mod p$.
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
4972
Mod of numbers with large exponents [modular order reduction]
93898
Prove that for any prime p, there is a complete set of mod p residues {q1, . . . , qp}, where each qi is prime.
35821
Infinitely many primes for quadratic residues
152231
Computing the product of p/(p - 2) over the odd primes
59416
Quadratic residues and index w.r.t. primitive root of a odd prime p
52530
There exists a prime congruent to $m$ mod $p$
46821
Finding roots in $\mathbb{Z}_p$
116585
$r$ primitive root of prime $p$, where $p \equiv 1 \mod 4$: prove $-r$ is also a primitive root
8784
modulo version of the quadratic formula and Euler's criterion
9787
Primitive roots modulo primes congruent to n!
60057
number of quadratic residues in finite field