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nth root of unity in a cyclic group $\mathbb{Z}_p^*$

score 1.5k · Answer 1 · 2026-03-29 11:44:13

1.5k

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nth root of unity in a cyclic group $\mathbb{Z}_p^*$

Published on 29 Mar 2026 - 11:44

score 112 · Answer 2 · 2015-12-16 21:05:56

112

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On multiplying symmetric matrices by diagonal matrices with roots of unity

Published on 16 Dec 2015 - 21:05

score 5.4k · Answer 3 · 2015-12-29 19:17:36

5.4k

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All Solutions for $(-256)^{\frac{1}{4}}$ and $1^{\frac{1}{5}}$ Imaginary Roots?

Published on 29 Dec 2015 - 19:17

score 36 · Answer 4 · 2015-12-29 19:46:06

36

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How can I choose $\frak p\unlhd\cal O$ prime so $u\in\cal O^\times$ becomes a $n$-th power (mod $\frak p$)?

Published on 29 Dec 2015 - 19:46

score 1.1k · Answer 5 · 2026-03-29 11:48:34

1.1k

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What is the sum of ALL of the nth powers of the qth roots of unity?

Published on 29 Mar 2026 - 11:48

score 75 · Answer 6 · 2016-01-02 10:39:35

75

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Why in a field of characteristic $p$, $\zeta_p \sqrt[p]t$ is not a root of $X^p-t\in \mathbb F_p(t)[X]$

Published on 02 Jan 2016 - 10:39

score 4.3k · Answer 7 · 2016-01-06 16:08:16

4.3k

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Why do I get an imaginary result for the cube root of a negative number?

Published on 06 Jan 2016 - 16:08

score 265 · Answer 8 · 2016-01-09 23:09:35

265

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What is the intersection of $\mathbb Z$ with the ideal generated by $1-\zeta_n$?

Published on 09 Jan 2016 - 23:09

score 251 · Answer 9 · 2016-01-18 13:56:49

251

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Find complex roots of $\frac{2i}{1+i}$

Published on 18 Jan 2016 - 13:56

score 151 · Answer 10 · 2016-01-22 10:23:50

151

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Why is the sum of the first $k$ powers of a $k$-th primitive root $\varphi_k$ of $1$ always $0$?

Published on 22 Jan 2016 - 10:23

score 1.2k · Answer 11 · 2016-01-29 04:26:21

1.2k

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Linear Combination of Roots of Unity

Published on 29 Jan 2016 - 4:26

score 116 · Answer 12 · 2016-02-04 23:41:51

116

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Show that the elements of the form $1+\zeta + \zeta^2 + \dots + \zeta^m$, with $1 \leq m \leq p-2$, are invertible in $\mathbb{Z}[\zeta]$

Published on 04 Feb 2016 - 23:41

score 271 · Answer 13 · 2026-03-28 22:36:56

271

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Finding $\sqrt{17}$ and $\sqrt{257}$ in the regular $17$-gon and $257$-gon?

Published on 28 Mar 2026 - 22:36

score 1.3k · Answer 14 · 2016-02-14 16:55:31

1.3k

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Finding fifth and tenth roots of unity in rectangular form.

Published on 14 Feb 2016 - 16:55

score 136 · Answer 15 · 2026-03-28 21:51:20

136

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Is there a theoretical (or practical) definition of $n$-gon, for $n < 0$?

Published on 28 Mar 2026 - 21:51

List Question

nth root of unity in a cyclic group $\mathbb{Z}_p^*$

On multiplying symmetric matrices by diagonal matrices with roots of unity

All Solutions for $(-256)^{\frac{1}{4}}$ and $1^{\frac{1}{5}}$ Imaginary Roots?

How can I choose $\frak p\unlhd\cal O$ prime so $u\in\cal O^\times$ becomes a $n$-th power (mod $\frak p$)?

What is the sum of ALL of the nth powers of the qth roots of unity?

Why in a field of characteristic $p$, $\zeta_p \sqrt[p]t$ is not a root of $X^p-t\in \mathbb F_p(t)[X]$

Why do I get an imaginary result for the cube root of a negative number?

What is the intersection of $\mathbb Z$ with the ideal generated by $1-\zeta_n$?

Find complex roots of $\frac{2i}{1+i}$

Why is the sum of the first $k$ powers of a $k$-th primitive root $\varphi_k$ of $1$ always $0$?

Linear Combination of Roots of Unity

Show that the elements of the form $1+\zeta + \zeta^2 + \dots + \zeta^m$, with $1 \leq m \leq p-2$, are invertible in $\mathbb{Z}[\zeta]$

Finding $\sqrt{17}$ and $\sqrt{257}$ in the regular $17$-gon and $257$-gon?

Finding fifth and tenth roots of unity in rectangular form.

Is there a theoretical (or practical) definition of $n$-gon, for $n < 0$?

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