Question

prove that $\zeta^{i}$ is a primitive root modulo p $\iff$ $\gcd(p-1,i) =1$ where $p$ is prime and $\zeta$ is a primitive root modulo p.

score 919 · Answer 1 · 2016-01-03 17:21:28

prove that $\zeta^{i}$ is a primitive root modulo p $\iff$ $\gcd(p-1,i) =1$ where $p$ is prime and $\zeta$ is a primitive root modulo p.

score 54 · Answer 2 · 2016-01-07 15:46:04

54

Views

Primitive root of unity with certain conditions

Published on 07 Jan 2016 - 15:46

score 513 · Answer 3 · 2026-03-27 22:47:37

513

Views

Primitive Root Mod P

Published on 27 Mar 2026 - 22:47

score 490 · Answer 4 · 2026-03-26 06:32:38

490

Views

How can I use primitive roots to prove that there are the same number of quadratic residues as non-residues?

Published on 26 Mar 2026 - 6:32

score 201 · Answer 5 · 2016-02-10 14:18:28

201

Views

Spliting subspaces and finite fields

Published on 10 Feb 2016 - 14:18

score 1k · Answer 6 · 2016-02-11 03:59:49

1k

Views

Show that $g^p (1 + p)$ is a primitive root modulo $p^e$

Published on 11 Feb 2016 - 3:59

score 245 · Answer 7 · 2016-02-12 06:14:55

245

Views

AMM 2488: Primitive Root Relatively Prime to p-1

Published on 12 Feb 2016 - 6:14

score 362 · Answer 8 · 2016-02-21 05:16:34

362

Views

Are there infinitely many pairs of primes, $p$ and $q$, such that $q = 4p + 1$?

Published on 21 Feb 2016 - 5:16

score 754 · Answer 9 · 2016-02-21 19:16:01

754

Views

When is 2 a primitive root for a Sophie Germain prime $p$ or its associate $2p + 1$?

Published on 21 Feb 2016 - 19:16

score 93 · Answer 10 · 2016-03-03 19:29:51

Let $p$ be an odd prime of the form $p=2^m+1$, for some positive integer $m$. Let $g$ be a primitive root mod $p$ with $1 \le g \le p$.

score 985 · Answer 11 · 2026-02-23 15:12:11

985

Views

Primitive roots generated from a primitive root

Published on 23 Feb 2026 - 15:12

score 293 · Answer 12 · 2016-04-03 18:27:31

293

Views

Product of three primitive roots mod prime number

Published on 03 Apr 2016 - 18:27

score 43 · Answer 13 · 2016-04-05 19:07:49

43

Views

$-1$ element in $\mathbb{Z}_n^$, where $n$ is such that $\mathbb{Z}_n^$ has a primitive root

Published on 05 Apr 2016 - 19:07

score 3.5k · Answer 14 · 2016-04-07 18:24:54

3.5k

Views

Find the Ф(28) = 12 primitive roots modulo 29...

Published on 07 Apr 2016 - 18:24

score 247 · Answer 15 · 2016-04-10 08:12:25

247

Views

Multiplication of three primitive roots

Published on 10 Apr 2016 - 8:12

List Question

prove that $\zeta^{i}$ is a primitive root modulo p $\iff$ $\gcd(p-1,i) =1$ where $p$ is prime and $\zeta$ is a primitive root modulo p.

Primitive root of unity with certain conditions

Primitive Root Mod P

How can I use primitive roots to prove that there are the same number of quadratic residues as non-residues?

Spliting subspaces and finite fields

Show that $g^p (1 + p)$ is a primitive root modulo $p^e$

AMM 2488: Primitive Root Relatively Prime to p-1

Are there infinitely many pairs of primes, $p$ and $q$, such that $q = 4p + 1$?

When is 2 a primitive root for a Sophie Germain prime $p$ or its associate $2p + 1$?

Let $p$ be an odd prime of the form $p=2^m+1$, for some positive integer $m$. Let $g$ be a primitive root mod $p$ with $1 \le g \le p$.

Primitive roots generated from a primitive root

Product of three primitive roots mod prime number

$-1$ element in $\mathbb{Z}_n^$, where $n$ is such that $\mathbb{Z}_n^$ has a primitive root

Find the Ф(28) = 12 primitive roots modulo 29...

Multiplication of three primitive roots

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