Question

If $f(x)=x^{m}+1$ is an irreducible polynomial in $\mathbb{F}_{p}[x]$, then prove that $2m$ divides $p^{m}-1$

score 109 · Answer 1 · 2015-06-02 22:43:36

109

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If $f(x)=x^{m}+1$ is an irreducible polynomial in $\mathbb{F}_{p}[x]$, then prove that $2m$ divides $p^{m}-1$

Published on 02 Jun 2015 - 22:43

score 5.6k · Answer 2 · 2015-06-02 23:11:47

5.6k

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Constructing a multiplication table for a finite field

Published on 02 Jun 2015 - 23:11

score 79 · Answer 3 · 2015-06-03 15:59:46

79

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Proof remainder of polynomial division GF(2) can be calculated by LSFR

Published on 03 Jun 2015 - 15:59

score 801 · Answer 4 · 2026-03-25 20:36:33

801

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In a vector space over a finite field, can the orbit of a point under matrix multiplication have dependent subsets?

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score 105 · Answer 5 · 2015-06-04 06:59:52

105

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Understanding an Opening to Finite Fields

Published on 04 Jun 2015 - 6:59

score 946 · Answer 6 · 2026-04-05 10:05:41

946

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Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$

Published on 05 Apr 2026 - 10:05

score 54 · Answer 7 · 2015-06-04 13:29:48

54

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How many quadratic non-residues are there in the image of $f(a) = a^2 - x^2$?

Published on 04 Jun 2015 - 13:29

score 46 · Answer 8 · 2015-06-06 05:21:42

46

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I need help with constructing the field GF$(2^8)$.

Published on 06 Jun 2015 - 5:21

score 2.1k · Answer 9 · 2015-06-06 07:51:28

2.1k

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Shortest irreducible polynomials over $\Bbb F_p$ of degree $n$

Published on 06 Jun 2015 - 7:51

score 436 · Answer 10 · 2015-06-06 21:22:10

436

Views

Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.

Published on 06 Jun 2015 - 21:22

score 1.3k · Answer 11 · 2026-03-29 03:53:30

1.3k

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Square root of $-1$ over a finite field

Published on 29 Mar 2026 - 3:53

score 2.4k · Answer 12 · 2015-06-07 15:04:56

2.4k

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Is every finite field a quotient ring of ${Z}[x]$?

Published on 07 Jun 2015 - 15:04

score 1k · Answer 13 · 2015-06-08 00:45:02

1k

Views

Newton's identities over finite fields

Published on 08 Jun 2015 - 0:45

score 874 · Answer 14 · 2015-06-08 12:20:16

874

Views

Find the multiplicative inverse of $a+1$ in $\mathbb{Z_2}(a)$.

Published on 08 Jun 2015 - 12:20

score 2.2k · Answer 15 · 2015-06-08 17:03:41

2.2k

Views

Finite fields and their subfields

Published on 08 Jun 2015 - 17:03

List Question

If $f(x)=x^{m}+1$ is an irreducible polynomial in $\mathbb{F}_{p}[x]$, then prove that $2m$ divides $p^{m}-1$

Constructing a multiplication table for a finite field

Proof remainder of polynomial division GF(2) can be calculated by LSFR

In a vector space over a finite field, can the orbit of a point under matrix multiplication have dependent subsets?

Understanding an Opening to Finite Fields

Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$

How many quadratic non-residues are there in the image of $f(a) = a^2 - x^2$?

I need help with constructing the field GF$(2^8)$.

Shortest irreducible polynomials over $\Bbb F_p$ of degree $n$

Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.

Square root of $-1$ over a finite field

Is every finite field a quotient ring of ${Z}[x]$?

Newton's identities over finite fields

Find the multiplicative inverse of $a+1$ in $\mathbb{Z_2}(a)$.

Finite fields and their subfields

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