List questions from roots-of-unity

Published on 25 Mar 2026 - 14:39

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How to show the degree $[\Bbb Q(\alpha _n+\frac{1}{\alpha_n}) : \Bbb Q]$ is $\phi(n)/2$, where $\alpha_n$ is a primitive $n$-th root of unity?

Published on 25 Mar 2026 - 14:46

1.4k

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Roots of unity notation

Published on 31 Mar 2017 - 23:05

648

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$x^p-a$ either has a root or is irreducible

Published on 06 Apr 2017 - 20:25

108

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Roots of unity in $\Bbb{Z}[X]/(X^2+X+1)^2$

Published on 26 Mar 2026 - 21:26

53

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Complex roots of arbitrary degree of the unity

Published on 08 Apr 2017 - 16:26

896

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Complex Numbers -- Find $z$ such that $(z+1)^6 = z^6.$

Published on 08 Apr 2017 - 16:57

108

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A magic basis of $\mathbb{C}^5$

Published on 08 Feb 2023 - 16:06

58

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is there a ring map from $\mathbb{Z}[e^{2\pi i/(p-1)}]$ to $\mathbb{Z}$ mod p where p prime?

Published on 25 Mar 2026 - 20:18

71

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When is $\sin(\frac{\pi}{p}) $ not expressible by "real radicals" and $\sin(\frac{\pi}{q_i}) $?

Published on 15 Feb 2023 - 23:11

324

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Third root of unity $\zeta$, extension degree of $\mathbb{Q}(\sqrt{2},\zeta)$, its $\mathbb{Q}$-Basis and extension of field morphism.

Published on 26 Feb 2023 - 18:33

126

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$\sin(\frac{\pi}{p}) $ not expressible by positive radicals and $\sin(\frac{\pi}{q_i})$ ??

Published on 26 Feb 2023 - 23:15

211

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Confusion about roots of unity over a field of characteristic $p$

Published on 28 Feb 2023 - 13:54

82

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Does $\sum_{j=1,j\neq k}^n\frac{z_k}{z_k-z_j}=\sum_{j=1,j\neq m}^n\frac{z_m}{z_m-z_j}$ implies the $(z_j)_{j=1,...,n}$ are the nth roots of $z_1^n$?

Published on 02 Mar 2023 - 20:40

22

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Primitive roots of unity modulo $q$

Published on 06 Mar 2023 - 9:59

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Cyclotomic Extension

How to show the degree $[\Bbb Q(\alpha _n+\frac{1}{\alpha_n}) : \Bbb Q]$ is $\phi(n)/2$, where $\alpha_n$ is a primitive $n$-th root of unity?

Roots of unity notation

$x^p-a$ either has a root or is irreducible

Roots of unity in $\Bbb{Z}[X]/(X^2+X+1)^2$

Complex roots of arbitrary degree of the unity

Complex Numbers -- Find $z$ such that $(z+1)^6 = z^6.$

A magic basis of $\mathbb{C}^5$

is there a ring map from $\mathbb{Z}[e^{2\pi i/(p-1)}]$ to $\mathbb{Z}$ mod p where p prime?

When is $\sin(\frac{\pi}{p}) $ not expressible by "real radicals" and $\sin(\frac{\pi}{q_i}) $?

Third root of unity $\zeta$, extension degree of $\mathbb{Q}(\sqrt{2},\zeta)$, its $\mathbb{Q}$-Basis and extension of field morphism.

$\sin(\frac{\pi}{p}) $ not expressible by positive radicals and $\sin(\frac{\pi}{q_i})$ ??

Confusion about roots of unity over a field of characteristic $p$

Does $\sum_{j=1,j\neq k}^n\frac{z_k}{z_k-z_j}=\sum_{j=1,j\neq m}^n\frac{z_m}{z_m-z_j}$ implies the $(z_j)_{j=1,...,n}$ are the nth roots of $z_1^n$?

Primitive roots of unity modulo $q$

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