Showing that $a$ is a primitive root modulo $p$
44729
Prove $g$ is a generator if $g^q=1 \pmod p$
50823
Primitive polynomials
103552
The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
115299
Elements of $\mathbb{F}_p$ having cube roots in $\mathbb{F}_p$
63493
Why 4 is not a primitive root modulo p for any prime p?
61860
Show that if $a$ has order $3\bmod p$ then $a+1$ has order $6\bmod p$.
40107
primitive n-th roots of unity
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
77820
Roots in a polynomial ring
100450
Prove that 3 is a primitive root of $7^k$ for all $k \ge 1$
147611
Given $P$ idempotent, show that $I-P$ is idempotent.
106091
Showing $\mathcal{P}(X)$ is isomorphic to $2^X$
20161
Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
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 $q$.
55621
Show that if $c_1, c_2, \ldots, c_{\phi(m)}$ is a reduced residue system modulo m, $m \neq 2$ then $c_1 + \cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$
93820
Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
130300
Proof that every quadratic residue has two roots, modulo a prime