Question

Find $\sum_{i=1}^{n-1}\frac{1}{2-a^i}$ if $1,a,a^2,...,a^{n-1}$ are the n$^\text{th}$ roots of unity

score 97 · Answer 1 · 2019-02-22 07:46:17

97

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Find $\sum_{i=1}^{n-1}\frac{1}{2-a^i}$ if $1,a,a^2,...,a^{n-1}$ are the n$^\text{th}$ roots of unity

Published on 22 Feb 2019 - 7:46

score 1.8k · Answer 2 · 2026-03-25 22:26:54

1.8k

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Degree of splitting field of $X^n-1$ over some finite field

Published on 25 Mar 2026 - 22:26

score 56 · Answer 3 · 2026-03-25 04:40:14

56

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About sums similar to gauss sums

Published on 25 Mar 2026 - 4:40

score 536 · Answer 4 · 2019-03-15 20:29:59

536

Views

Find a number field whose unit group is isomorphic to $\mathbb{Z}/4\mathbb{Z} \times \mathbb{Z}$

Published on 15 Mar 2019 - 20:29

score 5.6k · Answer 5 · 2026-03-25 11:13:23

5.6k

Views

Question about roots of unity in the Fast Fourier Transform

Published on 25 Mar 2026 - 11:13

score 50 · Answer 6 · 2019-03-20 14:20:36

50

Views

$a_i$ are the n-th roots of $1\in\mathbb{C}$, why does $(1-a_2)\cdot...\cdot(1-a_n)=n$?

Published on 20 Mar 2019 - 14:20

score 168 · Answer 7 · 2019-03-21 19:26:13

168

Views

Direct product decomposition of the group of complex roots of unity

Published on 21 Mar 2019 - 19:26

score 255 · Answer 8 · 2019-03-22 17:34:33

255

Views

Another Roots of Unity Sum

Published on 22 Mar 2019 - 17:34

score 76 · Answer 9 · 2019-03-30 19:02:32

76

Views

degree of extension re: roots of unity to the $2^n$ power and their conjugates

Published on 30 Mar 2019 - 19:02

score 96 · Answer 10 · 2019-04-01 20:32:29

96

Views

If $a$ is an $n$-th root of $z$ , $b$ is an $n$-th root of $w$, and $c$ is an $n$-th root of $zw$, then $ab=c$.

Published on 01 Apr 2019 - 20:32

score 36 · Answer 11 · 2019-04-04 15:01:43

36

Views

If $K$ is a subfield of $\mathbb{C}$ then $K(\zeta)/K$ is Galois

Published on 04 Apr 2019 - 15:01

score 108 · Answer 12 · 2019-04-11 04:39:04

108

Views

To find the sum: $\frac {1}{n!} \sum \binom {n}{2+3r} x^{1+r}$

Published on 11 Apr 2019 - 4:39

score 93 · Answer 13 · 2019-04-16 17:51:59

93

Views

Do there exist non-trivial integer coefficients that break linear independence of the roots of unity?

Published on 16 Apr 2019 - 17:51

score 59 · Answer 14 · 2019-04-20 15:34:56

59

Views

Complex roots of a complex polynomial

Published on 20 Apr 2019 - 15:34

score 68 · Answer 15 · 2019-04-21 06:07:30

68

Views

If $a \in \mathbb{C}$ and $\exists n \in \mathbb{N}$ s.t. $\{ a^n, a^{n+1} \} \in \mathbb{N}$, prove $a \in \mathbb{N}$

Published on 21 Apr 2019 - 6:07

List Question

Find $\sum_{i=1}^{n-1}\frac{1}{2-a^i}$ if $1,a,a^2,...,a^{n-1}$ are the n$^\text{th}$ roots of unity

Degree of splitting field of $X^n-1$ over some finite field

About sums similar to gauss sums

Find a number field whose unit group is isomorphic to $\mathbb{Z}/4\mathbb{Z} \times \mathbb{Z}$

Question about roots of unity in the Fast Fourier Transform

$a_i$ are the n-th roots of $1\in\mathbb{C}$, why does $(1-a_2)\cdot...\cdot(1-a_n)=n$?

Direct product decomposition of the group of complex roots of unity

Another Roots of Unity Sum

degree of extension re: roots of unity to the $2^n$ power and their conjugates

If $a$ is an $n$-th root of $z$ , $b$ is an $n$-th root of $w$, and $c$ is an $n$-th root of $zw$, then $ab=c$.

If $K$ is a subfield of $\mathbb{C}$ then $K(\zeta)/K$ is Galois

To find the sum: $\frac {1}{n!} \sum \binom {n}{2+3r} x^{1+r}$

Do there exist non-trivial integer coefficients that break linear independence of the roots of unity?

Complex roots of a complex polynomial

If $a \in \mathbb{C}$ and $\exists n \in \mathbb{N}$ s.t. $\{ a^n, a^{n+1} \} \in \mathbb{N}$, prove $a \in \mathbb{N}$

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