Question

Prove that if $r$ is a primitive root modulo $m$, and $(a, m) = (b, m) = 1$, then $r^a \equiv r^b \pmod{m}$ implies $a\equiv b \pmod{\varphi(m)}$

score 318 · Answer 1 · 2026-03-27 11:48:10

318

Views

Prove that if $r$ is a primitive root modulo $m$, and $(a, m) = (b, m) = 1$, then $r^a \equiv r^b \pmod{m}$ implies $a\equiv b \pmod{\varphi(m)}$

Published on 27 Mar 2026 - 11:48

score 395 · Answer 2 · 2026-03-27 10:10:05

395

Views

Let $p$ be an odd prime. Suppose that $a$ is an odd integer and also $a$ is a primitive root mod $p$. Show that $a$ is also a primitive root mod $2p$.

Published on 27 Mar 2026 - 10:10

score 158 · Answer 3 · 2016-11-01 21:52:52

158

Views

Is $g$ mod $p$ a generator for the multiplicative group mod $p^2$?

Published on 01 Nov 2016 - 21:52

score 2.8k · Answer 4 · 2016-11-06 01:44:11

2.8k

Views

Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$

Published on 06 Nov 2016 - 1:44

score 1.5k · Answer 5 · 2016-11-08 13:59:33

1.5k

Views

$m>2$ and $n > 2$ are relatively prime $\Rightarrow$ no primitive root of $mn$

Published on 08 Nov 2016 - 13:59

score 290 · Answer 6 · 2026-03-28 00:06:17

290

Views

Help with problem: Let $w$ a 15th-primitive-root of unity. Find all $n \in \Bbb N_{<0}$ such that $\sum_{i=0}^{n-1} w^{5i}=0$

Published on 28 Mar 2026 - 0:06

score 906 · Answer 7 · 2016-11-14 06:35:55

906

Views

If $r$ is a primitive root mod $p$ and $(r+tp)^{p-1} \not \equiv 1 \pmod{p^2}$, then $r+tp$ is a primitive root mod $p^k$

Published on 14 Nov 2016 - 6:35

score 1.3k · Answer 8 · 2016-11-18 05:14:43

1.3k

Views

Irreducible polynomial, Primitive Polynomial and Minimal Polynomial

Published on 18 Nov 2016 - 5:14

score 201 · Answer 9 · 2026-03-27 17:53:00

201

Views

Prove that if $g^{(p-1)/2} \equiv -1 (mod \mbox{ } p)$ then its smaller power can't be congruent to 1.

Published on 27 Mar 2026 - 17:53

score 1.2k · Answer 10 · 2016-11-28 18:12:08

1.2k

Views

Primitive Roots modulo $p^2$

Published on 28 Nov 2016 - 18:12

score 127 · Answer 11 · 2016-11-29 04:47:45

127

Views

Show that if ab has a primitive root with $(a,b) = 1$, then $a<3$ or $b<3$

Published on 29 Nov 2016 - 4:47

score 826 · Answer 12 · 2026-03-25 01:18:49

826

Views

How to use Hensel lemma to show that primitive root mod $p$ gives primitive root mod $p^2$ of the form $g + tp$

Published on 25 Mar 2026 - 1:18

score 74 · Answer 13 · 2026-03-28 01:48:43

74

Views

Find $\sum_{i=0}^{k-1}w^{in}$ in terms of $n \in \Bbb N$ being $w \in \Bbb C$ a k-th primitive root of unity.

Published on 28 Mar 2026 - 1:48

score 40 · Answer 14 · 2026-03-27 14:21:24

40

Views

Holomorphic function and deritives

Published on 27 Mar 2026 - 14:21

score 304 · Answer 15 · 2026-03-25 04:37:41

304

Views

Primitive elements of finite fields

Published on 25 Mar 2026 - 4:37

List Question

Prove that if $r$ is a primitive root modulo $m$, and $(a, m) = (b, m) = 1$, then $r^a \equiv r^b \pmod{m}$ implies $a\equiv b \pmod{\varphi(m)}$

Let $p$ be an odd prime. Suppose that $a$ is an odd integer and also $a$ is a primitive root mod $p$. Show that $a$ is also a primitive root mod $2p$.

Is $g$ mod $p$ a generator for the multiplicative group mod $p^2$?

Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$

$m>2$ and $n > 2$ are relatively prime $\Rightarrow$ no primitive root of $mn$

Help with problem: Let $w$ a 15th-primitive-root of unity. Find all $n \in \Bbb N_{<0}$ such that $\sum_{i=0}^{n-1} w^{5i}=0$

If $r$ is a primitive root mod $p$ and $(r+tp)^{p-1} \not \equiv 1 \pmod{p^2}$, then $r+tp$ is a primitive root mod $p^k$

Irreducible polynomial, Primitive Polynomial and Minimal Polynomial

Prove that if $g^{(p-1)/2} \equiv -1 (mod \mbox{ } p)$ then its smaller power can't be congruent to 1.

Primitive Roots modulo $p^2$

Show that if ab has a primitive root with $(a,b) = 1$, then $a<3$ or $b<3$

How to use Hensel lemma to show that primitive root mod $p$ gives primitive root mod $p^2$ of the form $g + tp$

Find $\sum_{i=0}^{k-1}w^{in}$ in terms of $n \in \Bbb N$ being $w \in \Bbb C$ a k-th primitive root of unity.

Holomorphic function and deritives

Primitive elements of finite fields

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