List questions from primitive-roots | MathQA

A primitive root modulo p is a primitive root modulo $p^2$ if and only if $g^{p-1} \not\equiv 1 \mod{p^2}$

Published on 30 Mar 2026 - 10:39

Order, primitive roots modulo 19

Published on 02 Oct 2022 - 17:17

Explicite upper bound for the smallest primitive root?

Published on 13 Oct 2022 - 16:14

Characterizing generators for the multiplicative group of a finite field.

Published on 01 Nov 2022 - 3:07

Calculation of generalized Artin's constants

Published on 03 Nov 2022 - 1:47

Show that the polynomial $x^4+x+1$ is primitive over $\mathbb{F}_2$

Published on 17 Nov 2022 - 18:15

Prove that the roots of cyclotomic polynomial $\Phi_{p-1}(x) \equiv 0 (mod~p)$ are exactly the primitive roots mod p

Published on 28 Mar 2026 - 11:35

How to prove that $\sum_\limits{k=1\\(k,p-1)=1}^{p-1}g^k \equiv \mu(p-1)$ (mod p) for prime p and primitive root g

Published on 20 Nov 2022 - 13:43

Finding primitive roots including negative sign

Published on 20 Nov 2022 - 20:23

Show that $2$ is not a primitive root of $8k + 7$

Published on 16 Dec 2022 - 13:35

$(a+pk)^{p-1}≡1+ph−pka^{p−2} \mod{p^2}$, for some $h∈\mathbb{Z}$; if $k≢ah \mod{p}$, then $a+pk$ is a primitive root mod $p^2$.

Published on 22 Jan 2023 - 0:14