Question

Schonhage-Strassen algorithm for multiplication of polynomials over a finite field (additive vs multiplicative complexity)

score 86 · Answer 1 · 2026-03-26 03:11:38

86

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Schonhage-Strassen algorithm for multiplication of polynomials over a finite field (additive vs multiplicative complexity)

Published on 26 Mar 2026 - 3:11

score 110 · Answer 2 · 2026-03-26 17:32:43

110

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Proving the locus of $P_k$ is an ellipse.

Published on 26 Mar 2026 - 17:32

score 125 · Answer 3 · 2023-05-17 06:14:06

125

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If $\sin(\pi/13)\sin(3\pi/13)\sin(4\pi/13)={a\over b}\sqrt{\frac{k-3\sqrt k}{2}}$, find $\frac{5a+b}{k}$.

Published on 17 May 2023 - 6:14

score 325 · Answer 4 · 2023-05-17 11:36:46

325

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If $f(x)$ is a monic polynomial in ${\mathbb Z}[x]$ and all roots have absolute value 1 , then all roots are roots of unity.

Published on 17 May 2023 - 11:36

score 76 · Answer 5 · 2023-05-24 09:02:09

76

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Computing a sum involving the roots of a tenth degree polynomial

Published on 24 May 2023 - 9:02

score 91 · Answer 6 · 2023-05-31 07:31:11

91

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Is there an element of order $n$ in all roots of $x^n - 1$ modulo $q$ where $q$ is a prime number and $n \mid q-1$

Published on 31 May 2023 - 7:31

score 196 · Answer 7 · 2023-06-03 10:02:44

196

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Zeros of a complex function on the unit circle

Published on 03 Jun 2023 - 10:02

score 74 · Answer 8 · 2026-03-27 17:53:03

74

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length of side of a regular $n$-gon is less than length of any diagonal

Published on 27 Mar 2026 - 17:53

score 47 · Answer 9 · 2026-03-25 16:20:35

47

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Doubt in Cyclotomic Fields and polynomials

Published on 25 Mar 2026 - 16:20

score 100 · Answer 10 · 2023-07-07 01:52:34

100

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Roots of Unity Sum Proof

Published on 07 Jul 2023 - 1:52

score 48 · Answer 11 · 2023-07-13 15:03:02

48

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$P(z)=4z^4+az^3+bz^2+cz+d$ where $0\le d\le c\le b\le a\le 4$ has a zero $z_0$ of magnitude $1$. Find the sum of $P(1)$s of all such polynomials $P$.

Published on 13 Jul 2023 - 15:03

score 46 · Answer 12 · 2023-07-15 04:40:11

46

Views

Number of Distinct Roots of Unity

Published on 15 Jul 2023 - 4:40

score 182 · Answer 13 · 2023-07-16 18:42:15

182

Views

IMO proposal question. prove $\sum_{k=1}^{n} k \cos(\frac{2 \pi a_k} n) = 0$

Published on 16 Jul 2023 - 18:42

score 113 · Answer 14 · 2023-07-26 13:16:48

113

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Prove $\prod_{k = 1}^{n - 1}(x - e^{\frac{2\pi ik}{n}}) = \frac{x^n - 1}{x - 1}$

Published on 26 Jul 2023 - 13:16

score 154 · Answer 15 · 2023-08-03 03:33:34

154

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Given $\theta$, how to check if $e^{i\theta}$ a root of unity?

Published on 03 Aug 2023 - 3:33

List Question

Schonhage-Strassen algorithm for multiplication of polynomials over a finite field (additive vs multiplicative complexity)

Proving the locus of $P_k$ is an ellipse.

If $\sin(\pi/13)\sin(3\pi/13)\sin(4\pi/13)={a\over b}\sqrt{\frac{k-3\sqrt k}{2}}$, find $\frac{5a+b}{k}$.

If $f(x)$ is a monic polynomial in ${\mathbb Z}[x]$ and all roots have absolute value 1 , then all roots are roots of unity.

Computing a sum involving the roots of a tenth degree polynomial

Is there an element of order $n$ in all roots of $x^n - 1$ modulo $q$ where $q$ is a prime number and $n \mid q-1$

Zeros of a complex function on the unit circle

length of side of a regular $n$-gon is less than length of any diagonal

Doubt in Cyclotomic Fields and polynomials

Roots of Unity Sum Proof

$P(z)=4z^4+az^3+bz^2+cz+d$ where $0\le d\le c\le b\le a\le 4$ has a zero $z_0$ of magnitude $1$. Find the sum of $P(1)$s of all such polynomials $P$.

Number of Distinct Roots of Unity

IMO proposal question. prove $\sum_{k=1}^{n} k \cos(\frac{2 \pi a_k} n) = 0$

Prove $\prod_{k = 1}^{n - 1}(x - e^{\frac{2\pi ik}{n}}) = \frac{x^n - 1}{x - 1}$

Given $\theta$, how to check if $e^{i\theta}$ a root of unity?

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