List questions from roots-of-unity

Published on 07 Jan 2021 - 10:48

145

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Gaussian like sum with binomial coefficients

Published on 25 Mar 2026 - 16:20

52

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Prove $\prod_{k=0}^{n-1}(a+b\varepsilon^2_k)=a^n+b^n$.

Published on 13 Jan 2021 - 0:47

618

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Proving a function is operation preserving

Published on 16 Jan 2021 - 23:04

56

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$\varphi(d)$ elements of order $d$ in $\mathbb{U}_n$ (defined in the question)

Published on 01 Apr 2026 - 3:11

474

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How to solve $(z-1)^n=(z+1)^n$

Published on 03 Feb 2021 - 22:48

96

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Infinitely many pairs $(a,b)$ where if r is a root it's inverse is also a root.

Published on 07 Feb 2021 - 1:56

65

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Solutions to sum of exponential

Published on 10 Feb 2021 - 7:02

313

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Why are roots of unity always distinct?

Published on 10 Feb 2021 - 7:33

55

Views

Are there $x_n$'s and $y_n$'s such that $\sum_{n=1}^Ne^{-i2m\pi x_n}=\sum_{n=1}^Ne^{-i2m\pi y_n}$ for $1\geq x_n>y_n\geq0$

Published on 10 Feb 2021 - 19:49

48

Views

Why is $i^{4/3}$ not equal to 1?

Published on 20 Feb 2021 - 12:21

635

Views

Finding the fifth roots of unity using DeMoivre's theorem. I'm getting $-1$ as a root twice.

Published on 22 Feb 2021 - 4:46

77

Views

Determine the generator for the cyclic group formed by the solutions of $x^9 = 1$.

Published on 29 Mar 2026 - 23:34

1.8k

Views

Solutions to $z^5-1=0$ using "root of unity"?

Published on 23 Feb 2021 - 2:48

279

Views

Why is $2$-adic roots of unity $\{1,-1\}$

Published on 26 Feb 2021 - 5:09

List Question

$n$th root of $\alpha$

Gaussian like sum with binomial coefficients

Prove $\prod_{k=0}^{n-1}(a+b\varepsilon^2_k)=a^n+b^n$.

Proving a function is operation preserving

$\varphi(d)$ elements of order $d$ in $\mathbb{U}_n$ (defined in the question)

How to solve $(z-1)^n=(z+1)^n$

Infinitely many pairs $(a,b)$ where if r is a root it's inverse is also a root.

Solutions to sum of exponential

Why are roots of unity always distinct?

Are there $x_n$'s and $y_n$'s such that $\sum_{n=1}^Ne^{-i2m\pi x_n}=\sum_{n=1}^Ne^{-i2m\pi y_n}$ for $1\geq x_n>y_n\geq0$

Why is $i^{4/3}$ not equal to 1?

Finding the fifth roots of unity using DeMoivre's theorem. I'm getting $-1$ as a root twice.

Determine the generator for the cyclic group formed by the solutions of $x^9 = 1$.

Solutions to $z^5-1=0$ using "root of unity"?

Why is $2$-adic roots of unity $\{1,-1\}$

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