Question

Are all roots of unity (solutions to $a^k \equiv 1$) for a prime modulo $p$, a multiple of $p-1$??

score 39 · Answer 1 · 2015-02-15 00:31:47

39

Views

Are all roots of unity (solutions to $a^k \equiv 1$) for a prime modulo $p$, a multiple of $p-1$??

Published on 15 Feb 2015 - 0:31

score 167 · Answer 2 · 2015-02-15 23:22:32

167

Views

Why is $\mathbb F_5(\root{15}\of t)$ not normal over $\mathbb F_5(t)$?

Published on 15 Feb 2015 - 23:22

score 128 · Answer 3 · 2026-03-25 06:11:04

128

Views

Roots of unit in a DVR

Published on 25 Mar 2026 - 6:11

score 550 · Answer 4 · 2015-02-21 23:05:33

550

Views

To prove: $ [K : \mathbb{Q}] = 2 \ \Longrightarrow \ \exists \zeta \text{ primitive root of unity}, \ \mathbb{Q}(\zeta) \ \supseteq \ K $

Published on 21 Feb 2015 - 23:05

score 299 · Answer 5 · 2015-02-22 22:20:19

299

Views

To prove: For $p$ prime, $\zeta \in \mathbb{C}*$ and $ord(\zeta) = p$, $(1-\zeta)$ is a prime ideal in $\mathbb{Z}[\zeta]$

Published on 22 Feb 2015 - 22:20

score 524 · Answer 6 · 2015-02-25 22:58:45

524

Views

A Polygon is inscribed in a circle $\Gamma$

Published on 25 Feb 2015 - 22:58

score 99 · Answer 7 · 2015-02-26 20:50:33

99

Views

for $p$ given, $\zeta_p$ a primitive root of unity, fow which $d\in \mathbb{Z}$ does $\zeta_p \in \mathbb{Q}(\sqrt{d})$?

Published on 26 Feb 2015 - 20:50

score 954 · Answer 8 · 2015-03-08 20:57:19

954

Views

Why is $\sqrt [n] 1$ not an expression "in radicals" of a root of unity?

Published on 08 Mar 2015 - 20:57

score 414 · Answer 9 · 2015-03-09 10:37:54

414

Views

Requirement on Norm for units in Cyclotomic Fields

Published on 09 Mar 2015 - 10:37

score 948 · Answer 10 · 2015-03-10 08:38:12

948

Views

Finding units in cyclotomic fields

Published on 10 Mar 2015 - 8:38

score 177 · Answer 11 · 2015-03-16 01:04:44

177

Views

Prove: there is a unique pair of integer roots of unity which differ in real part by $1$.

Published on 16 Mar 2015 - 1:04

score 114 · Answer 12 · 2015-03-20 21:31:33

114

Views

Carmichael numbers and primitive roots of unity

Published on 20 Mar 2015 - 21:31

score 246 · Answer 13 · 2026-03-22 11:35:39

246

Views

Carmichael function and primitive roots of unity

Published on 22 Mar 2026 - 11:35

score 429 · Answer 14 · 2015-04-06 05:46:20

429

Views

Roots of unity of an odd degree number field

Published on 06 Apr 2015 - 5:46

score 379 · Answer 15 · 2015-04-09 10:38:11

379

Views

number of roots of unity which satisfy a given polynomial

Published on 09 Apr 2015 - 10:38

List Question

Are all roots of unity (solutions to $a^k \equiv 1$) for a prime modulo $p$, a multiple of $p-1$??

Why is $\mathbb F_5(\root{15}\of t)$ not normal over $\mathbb F_5(t)$?

Roots of unit in a DVR

To prove: $ [K : \mathbb{Q}] = 2 \ \Longrightarrow \ \exists \zeta \text{ primitive root of unity}, \ \mathbb{Q}(\zeta) \ \supseteq \ K $

To prove: For $p$ prime, $\zeta \in \mathbb{C}*$ and $ord(\zeta) = p$, $(1-\zeta)$ is a prime ideal in $\mathbb{Z}[\zeta]$

A Polygon is inscribed in a circle $\Gamma$

for $p$ given, $\zeta_p$ a primitive root of unity, fow which $d\in \mathbb{Z}$ does $\zeta_p \in \mathbb{Q}(\sqrt{d})$?

Why is $\sqrt [n] 1$ not an expression "in radicals" of a root of unity?

Requirement on Norm for units in Cyclotomic Fields

Finding units in cyclotomic fields

Prove: there is a unique pair of integer roots of unity which differ in real part by $1$.

Carmichael numbers and primitive roots of unity

Carmichael function and primitive roots of unity

Roots of unity of an odd degree number field

number of roots of unity which satisfy a given polynomial

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