Primitive roots: If $p$ is a prime such that $p\equiv 1 \pmod 4$, and $a$ is a primitive root, then $-a$ is also a primitive root.
116585
$r$ primitive root of prime $p$, where $p \equiv 1 \mod 4$: prove $-r$ is also a primitive root
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
128575
Elementary proof that $3$ is a primitive root of a Fermat prime?
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
134916
When g and -g are both primitive roots
140948
Suppose $p$ and $q$ are odd primes and $p = q + 4a$ for some $a$. Prove that $(\frac ap) = (\frac aq)$ holds.
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
104484
Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$
32618
Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$
153862
A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime.
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
138941
If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p.
28644
For $q, p$ odd primes such that $p \neq q$, there is not primitive root modulo $pq$.
39719
If $g$ is a primitive root of $p^2$ where $p$ is an odd prime, why is $g$ a primitive root of $p^k$ for any $k \geq 1$?
63493
Why 4 is not a primitive root modulo p for any prime p?
17919
For every prime of the form $2^{4n}+1$, 7 is a primitive root.
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$