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Niti
Niti
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3-rd roots nontrivial cube root of unity over finite fields

Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2 = Fp[x]Fp^2[x]/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: (p-1)/2 + (3^((p+1)/4)) mod(p))*i where i^2=-1. But it seems not to be correct: Any idea?

3-rd roots of unity over finite fields

Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2 = Fp[x]/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: (p-1)/2 + (3^((p+1)/4)) mod(p))*i where i^2=-1. But it seems not to be correct: Any idea?

nontrivial cube root of unity

Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2 = Fp^2[x]/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: (p-1)/2 + (3^((p+1)/4)) mod(p))*i where i^2=-1. But it seems not to be correct: Any idea?

Post Closed as "off topic" by Franz Lemmermeyer, Zev Chonoles, Mariano Suárez-Álvarez, Daniel Litt, Felipe Voloch
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Charles Matthews
Charles Matthews
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Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2 = Fp[x]/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: (p-1)/2 + (3^((p+1)/4)) mod(p))*i where i^2=-1. But it seems not to be correct: Any idea?

Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: (p-1)/2 + (3^((p+1)/4)) mod(p))*i where i^2=-1. But it seems not to be correct: Any idea?

Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2 = Fp[x]/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: (p-1)/2 + (3^((p+1)/4)) mod(p))*i where i^2=-1. But it seems not to be correct: Any idea?

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Niti
Niti
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Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: x = (p-1)/2, 3^ + (3^((p+1)/4)) mod(p))*i where i^2=-1. But it seems not to be correct: Any idea?

Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: x = (p-1/2, 3^((p+1)/4)) mod(p). But it seems not to be correct: Any idea?

Hi,

I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2/(x^2+1). So, i need x where x^3=1.

Somehow I came into a source saying that it would be: (p-1)/2 + (3^((p+1)/4)) mod(p))*i where i^2=-1. But it seems not to be correct: Any idea?

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Niti
Niti
  • 3
  • 3