Question

Let $w \in G_{15}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $\sum_{i=2}^{n-1} w^{3i} = 0$

score 37 · Answer 1 · 2026-03-25 15:28:11

37

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Let $w \in G_{15}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $\sum_{i=2}^{n-1} w^{3i} = 0$

Published on 25 Mar 2026 - 15:28

score 175 · Answer 2 · 2019-06-17 09:47:26

175

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Complex roots of unity: Proof

Published on 17 Jun 2019 - 9:47

score 1.2k · Answer 3 · 2026-03-26 14:43:16

1.2k

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Solutions of $x^2 \equiv 1 \pmod N$

Published on 26 Mar 2026 - 14:43

score 44 · Answer 4 · 2019-06-20 05:17:41

44

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Find every $a \in \mathbb{R}$ such that $f = X^{2n+1} - (2n+1)X + a$ has a repeated root

Published on 20 Jun 2019 - 5:17

score 546 · Answer 5 · 2019-06-20 13:45:22

546

Views

Using roots of unity to find exact trig values

Published on 20 Jun 2019 - 13:45

score 37 · Answer 6 · 2019-06-22 06:14:13

37

Views

Let $w \in G_{24}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $w^{15n} + \sum^{11}_{i=1} \overline{w}^{2i+6}$ is purely imaginary.

Published on 22 Jun 2019 - 6:14

score 37 · Answer 7 · 2019-06-23 23:58:49

37

Views

Polynomial for product over a set

Published on 23 Jun 2019 - 23:58

score 155 · Answer 8 · 2026-03-25 03:21:19

155

Views

Rational coefficients of the prime roots of unity (basis set in $\mathbb{Q}$).

Published on 25 Mar 2026 - 3:21

score 68 · Answer 9 · 2019-07-04 00:18:46

68

Views

Find all $w \in G_{28}$ such that $1 + w^2 + w^4 + w^6 =0$

Published on 04 Jul 2019 - 0:18

score 50 · Answer 10 · 2019-07-04 02:17:34

50

Views

How to isolate terms in a polynomial based on their exponent?

Published on 04 Jul 2019 - 2:17

score 33 · Answer 11 · 2026-03-25 16:46:24

33

Views

Let $w \in G_{63}$ be a primitive root of unity. Find all $n\geq 6$ such that $\sum_{k=6}^n w^{35k} = 0$ and $w^{12n} = w^{15}$

Published on 25 Mar 2026 - 16:46

score 287 · Answer 12 · 2019-07-11 18:15:49

287

Views

Upper bound for sum of the nth roots of unity

Published on 11 Jul 2019 - 18:15

score 68 · Answer 13 · 2019-07-15 00:14:21

68

Views

Solution to $\frac{d^n y}{dx^n} = y$ for integer $n$

Published on 15 Jul 2019 - 0:14

score 155 · Answer 14 · 2026-03-25 23:58:46

155

Views

How to show that the splitting field of $x^7 - 5$ over $\mathbb{Q}$ is equal to $\mathbb{Q}(\sqrt[7]{5}, \exp(2\pi i/7))$?

Published on 25 Mar 2026 - 23:58

score 362 · Answer 15 · 2019-07-25 15:29:12

362

Views

$\omega = \frac{1 + \sqrt3 i}{2}$ , $ \omega^5 = ? $

Published on 25 Jul 2019 - 15:29

List Question

Let $w \in G_{15}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $\sum_{i=2}^{n-1} w^{3i} = 0$

Complex roots of unity: Proof

Solutions of $x^2 \equiv 1 \pmod N$

Find every $a \in \mathbb{R}$ such that $f = X^{2n+1} - (2n+1)X + a$ has a repeated root

Using roots of unity to find exact trig values

Let $w \in G_{24}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $w^{15n} + \sum^{11}_{i=1} \overline{w}^{2i+6}$ is purely imaginary.

Polynomial for product over a set

Rational coefficients of the prime roots of unity (basis set in $\mathbb{Q}$).

Find all $w \in G_{28}$ such that $1 + w^2 + w^4 + w^6 =0$

How to isolate terms in a polynomial based on their exponent?

Let $w \in G_{63}$ be a primitive root of unity. Find all $n\geq 6$ such that $\sum_{k=6}^n w^{35k} = 0$ and $w^{12n} = w^{15}$

Upper bound for sum of the nth roots of unity

Solution to $\frac{d^n y}{dx^n} = y$ for integer $n$

How to show that the splitting field of $x^7 - 5$ over $\mathbb{Q}$ is equal to $\mathbb{Q}(\sqrt[7]{5}, \exp(2\pi i/7))$?

$\omega = \frac{1 + \sqrt3 i}{2}$ , $ \omega^5 = ? $

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