Question

Prove that $a$ is a primitive root $\bmod{p}$ if and only if $-a$ has order $\frac{p-1}{2}$

score 2.3k · Answer 1 · 2015-04-01 16:32:31

2.3k

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Prove that $a$ is a primitive root $\bmod{p}$ if and only if $-a$ has order $\frac{p-1}{2}$

Published on 01 Apr 2015 - 16:32

score 3.9k · Answer 2 · 2015-04-07 05:20:44

3.9k

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Finding order of an integer with (mod 9)?

Published on 07 Apr 2015 - 5:20

score 555 · Answer 3 · 2026-03-28 04:01:52

555

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primitive roots and quadratic residues

Published on 28 Mar 2026 - 4:01

score 507 · Answer 4 · 2015-04-11 20:39:21

507

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Proving $\frac{p-1}{2}$ is a primitive root modulo $p$ if and only if $2(-1)^{(p-1)/2}$ is a primitive root modulo $p$

Published on 11 Apr 2015 - 20:39

score 87 · Answer 5 · 2015-04-11 20:44:08

87

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$g^q-q$ and $g^q-gq$ are primitive roots modulo $q^2$

Published on 11 Apr 2015 - 20:44

score 1.9k · Answer 6 · 2026-03-25 10:58:32

1.9k

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How is $3$ not a primitive root mod 8?

Published on 25 Mar 2026 - 10:58

score 116 · Answer 7 · 2015-05-01 12:52:36

116

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If $p$ is an odd prime with $(p - 1)/2$ primitive roots, is $p$ a Fermat prime?

Published on 01 May 2015 - 12:52

score 273 · Answer 8 · 2015-05-02 19:10:53

273

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Why is $c+q$ still a primitive root modulo $q$?

Published on 02 May 2015 - 19:10

score 73 · Answer 9 · 2026-03-25 19:03:10

73

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A multivalued function $ f(x) = 0 $ with integer solutions $ x_1=p(n) $ and $x_2=q(n) $

Published on 25 Mar 2026 - 19:03

score 69 · Answer 10 · 2015-05-08 00:45:52

69

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Proof for primality based on exponents and primitive roots

Published on 08 May 2015 - 0:45

score 688 · Answer 11 · 2015-05-10 21:07:01

688

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Proof of primitive roots in $F_{128}$

Published on 10 May 2015 - 21:07

score 2.3k · Answer 12 · 2015-05-15 05:09:11

2.3k

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Online primitive root modulo n list or tool?

Published on 15 May 2015 - 5:09

score 666 · Answer 13 · 2015-05-15 09:03:16

666

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Conjecture about the product of the primitive roots modulo a prime number ($\prod Pr_p$)

Published on 15 May 2015 - 9:03

score 1.5k · Answer 14 · 2015-05-18 02:04:36

1.5k

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What does "maximum order elements to mod n" mean for a number n without primitive roots modulo n?

Published on 18 May 2015 - 2:04

score 122 · Answer 15 · 2015-05-20 03:56:27

122

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Is there a counterexample? $\forall p \in \Bbb P\ ,\ p\gt 61\ ,\ \exists\ r1,r2\ \in \{\ Primitive\ Roots\ Modulo\ p\ \}\ /\ r1+r2 = NextPrime(p)$

Published on 20 May 2015 - 3:56

List Question

Prove that $a$ is a primitive root $\bmod{p}$ if and only if $-a$ has order $\frac{p-1}{2}$

Finding order of an integer with (mod 9)?

primitive roots and quadratic residues

Proving $\frac{p-1}{2}$ is a primitive root modulo $p$ if and only if $2(-1)^{(p-1)/2}$ is a primitive root modulo $p$

$g^q-q$ and $g^q-gq$ are primitive roots modulo $q^2$

How is $3$ not a primitive root mod 8?

If $p$ is an odd prime with $(p - 1)/2$ primitive roots, is $p$ a Fermat prime?

Why is $c+q$ still a primitive root modulo $q$?

A multivalued function $ f(x) = 0 $ with integer solutions $ x_1=p(n) $ and $x_2=q(n) $

Proof for primality based on exponents and primitive roots

Proof of primitive roots in $F_{128}$

Online primitive root modulo n list or tool?

Conjecture about the product of the primitive roots modulo a prime number ($\prod Pr_p$)

What does "maximum order elements to mod n" mean for a number n without primitive roots modulo n?

Is there a counterexample? $\forall p \in \Bbb P\ ,\ p\gt 61\ ,\ \exists\ r1,r2\ \in \{\ Primitive\ Roots\ Modulo\ p\ \}\ /\ r1+r2 = NextPrime(p)$

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