List questions from roots-of-unity

Published on 09 Oct 2022 - 22:11

332

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A smarter (not bashy) way to solve this roots of unity problem?

Published on 01 Apr 2026 - 15:07

620

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Show that all the nonzero roots of $f(x)$ are roots of unity. (A theorem of Kronecker)

Published on 10 Oct 2022 - 13:18

49

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What is the least degree rational polynomial which has $e^{2 \pi i/15}$ as one of its roots?

Published on 14 Oct 2022 - 18:32

109

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A number-theoretic problem involving 5th roots of unity

Published on 16 Oct 2022 - 16:42

116

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Cyclic group of roots of unity.

Published on 21 Oct 2022 - 5:19

68

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Characterizing generators for the multiplicative group of a finite field.

Published on 30 Mar 2026 - 13:43

178

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How does the extension field $F_{p^k}$ contain complex roots of unity?

Published on 27 Mar 2026 - 2:37

75

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How many n-th roots of unity are there in a finite field?

Published on 03 Nov 2022 - 5:04

74

Views

Show by specifying an isomorphism that the group of sixth unit roots $\mu_6$ is isomorphic to the subgroup

Published on 05 Nov 2022 - 12:53

195

Views

Find All Complex solutions for $z^3+3i\bar{z}=0$

Published on 16 Nov 2022 - 17:03

110

Views

Suggestion or handout for (generating + roots of unity filter)

Published on 22 Nov 2022 - 0:51

46

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If $u$ is an $n$-th root of unity, $p$ is a prime number such that $p \nmid n$, then $P(u^p)=0$ where $P$ is the minimal polynomial of $u$

Published on 28 Mar 2026 - 11:35

33

Views

$\xi_p^i-\xi_p^j$ divides $p$ in the ring $\mathbb{Z}[\xi_p]$

Published on 26 Mar 2026 - 16:06

45

Views

Minimum of a finite Fourier sum

Published on 09 Dec 2022 - 20:01

List Question

What is the summation of $^nC_1 + ^nC_4 + ^nC_7+ \ldots$?

A smarter (not bashy) way to solve this roots of unity problem?

Show that all the nonzero roots of $f(x)$ are roots of unity. (A theorem of Kronecker)

What is the least degree rational polynomial which has $e^{2 \pi i/15}$ as one of its roots?

A number-theoretic problem involving 5th roots of unity

Cyclic group of roots of unity.

Characterizing generators for the multiplicative group of a finite field.

How does the extension field $F_{p^k}$ contain complex roots of unity?

How many n-th roots of unity are there in a finite field?

Show by specifying an isomorphism that the group of sixth unit roots $\mu_6$ is isomorphic to the subgroup

Find All Complex solutions for $z^3+3i\bar{z}=0$

Suggestion or handout for (generating + roots of unity filter)

If $u$ is an $n$-th root of unity, $p$ is a prime number such that $p \nmid n$, then $P(u^p)=0$ where $P$ is the minimal polynomial of $u$

$\xi_p^i-\xi_p^j$ divides $p$ in the ring $\mathbb{Z}[\xi_p]$

Minimum of a finite Fourier sum

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