Question

Showing that roots common to $z^m-1=0$ and $z^n-1=0$ where $\gcd(m,n)=d$ are given by all roots of $z^{d}-1=0$

score 41 · Answer 1 · 2021-06-02 19:24:35

41

Views

Showing that roots common to $z^m-1=0$ and $z^n-1=0$ where $\gcd(m,n)=d$ are given by all roots of $z^{d}-1=0$

Published on 02 Jun 2021 - 19:24

score 42 · Answer 2 · 2021-06-06 11:37:40

42

Views

Minimize sum of $k$ distinct $n$-th roots of unity.

Published on 06 Jun 2021 - 11:37

score 67 · Answer 3 · 2021-06-06 19:29:16

67

Views

Number of roots of unity in a finite cyclic group G, source to cite

Published on 06 Jun 2021 - 19:29

score 68 · Answer 4 · 2021-06-08 13:15:06

68

Views

Cyclic codes and roots of unity

Published on 08 Jun 2021 - 13:15

score 59 · Answer 5 · 2026-03-26 07:59:06

59

Views

How to use the Bezout identity in the $mn$-th roots of unity?

Published on 26 Mar 2026 - 7:59

score 69 · Answer 6 · 2021-06-26 16:43:05

69

Views

Real numbers having the form $\sqrt[p]{2021+\sqrt[q]{a}}$ that can be written as linear combinations of some roots of unity.

Published on 26 Jun 2021 - 16:43

score 510 · Answer 7 · 2026-04-01 02:29:28

510

Views

How would one solve $z^6+z^4+z^3+z^2+1=0$?

Published on 01 Apr 2026 - 2:29

score 150 · Answer 8 · 2021-07-02 16:36:33

150

Views

Asymptotics for $\sum_{k=0}^{n-1}(-1)^k \cot(\frac{2k+1}{4n}\pi)\log{(2\sin(\frac{2k+1}{4n}\pi))} $

Published on 02 Jul 2021 - 16:36

score 349 · Answer 9 · 2026-03-31 07:48:51

349

Views

Condition that a polygon is regular in the complex plane

Published on 31 Mar 2026 - 7:48

score 137 · Answer 10 · 2021-07-04 13:11:40

137

Views

How to convert $\alpha = \cos(\frac{8\pi}{11})+ i \sin(\frac{8\pi}{11})$ into $\text{n}^{th}$ roots of unity format?

Published on 04 Jul 2021 - 13:11

score 154 · Answer 11 · 2021-07-19 06:17:53

154

Views

Proving $x^2 + x + 1$ is a factor of $P_n (x)=(x+1)^{2n+1} + x^{n+2}$.

Published on 19 Jul 2021 - 6:17

score 56 · Answer 12 · 2021-07-19 12:37:39

56

Views

What is wrong with these quadratics?

Published on 19 Jul 2021 - 12:37

score 55 · Answer 13 · 2026-03-30 05:25:32

55

Views

Stuck at the end with a trigonometric series

Published on 30 Mar 2026 - 5:25

score 153 · Answer 14 · 2021-07-29 21:01:28

153

Views

$\tan\frac{\pi}{9} +4\sin\frac{\pi}{9} = \sqrt 3 $

Published on 29 Jul 2021 - 21:01

score 110 · Answer 15 · 2026-03-30 08:36:49

110

Views

Why it is sufficient to look at prime divisor of $p-1$ when finding generators of $\mathbb{Z}_p^*$?

Published on 30 Mar 2026 - 8:36

List Question

Showing that roots common to $z^m-1=0$ and $z^n-1=0$ where $\gcd(m,n)=d$ are given by all roots of $z^{d}-1=0$

Minimize sum of $k$ distinct $n$-th roots of unity.

Number of roots of unity in a finite cyclic group G, source to cite

Cyclic codes and roots of unity

How to use the Bezout identity in the $mn$-th roots of unity?

Real numbers having the form $\sqrt[p]{2021+\sqrt[q]{a}}$ that can be written as linear combinations of some roots of unity.

How would one solve $z^6+z^4+z^3+z^2+1=0$?

Asymptotics for $\sum_{k=0}^{n-1}(-1)^k \cot(\frac{2k+1}{4n}\pi)\log{(2\sin(\frac{2k+1}{4n}\pi))} $

Condition that a polygon is regular in the complex plane

How to convert $\alpha = \cos(\frac{8\pi}{11})+ i \sin(\frac{8\pi}{11})$ into $\text{n}^{th}$ roots of unity format?

Proving $x^2 + x + 1$ is a factor of $P_n (x)=(x+1)^{2n+1} + x^{n+2}$.

What is wrong with these quadratics?

Stuck at the end with a trigonometric series

$\tan\frac{\pi}{9} +4\sin\frac{\pi}{9} = \sqrt 3 $

Why it is sufficient to look at prime divisor of $p-1$ when finding generators of $\mathbb{Z}_p^*$?

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