Question

Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$

score 824 · Answer 1 · 2026-03-20 06:55:54

824

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Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$

Published on 20 Mar 2026 - 6:55

score 844 · Answer 2 · 2026-03-17 20:07:15

844

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Period of a binary sequence

Published on 17 Mar 2026 - 20:07

score 51 · Answer 3 · 2026-03-22 14:09:38

51

Views

Order of $x$ in $\mathbb F_q[x]/(g(x))$

Published on 22 Mar 2026 - 14:09

score 93 · Answer 4 · 2018-01-29 22:05:59

93

Views

Prove that this quadratically closed extension of $\mathbb{F}_2$ remains quadratically closed after considering cubic extensions

Published on 29 Jan 2018 - 22:05

score 85 · Answer 5 · 2018-01-30 14:51:21

85

Views

What is the dimension of $\mathbb{R}^2$ over $\mathbb{F}_3$?

Published on 30 Jan 2018 - 14:51

score 38 · Answer 6 · 2018-01-31 05:18:31

38

Views

How to show that there are no roots of $x^{q+1}+1$ in a finite field of size $q$

Published on 31 Jan 2018 - 5:18

score 1.6k · Answer 7 · 2026-03-24 22:13:58

1.6k

Views

Factorization of $x^7 - 1$ into irreducible polynomials over $\Bbb{F_2}[x]$

Published on 24 Mar 2026 - 22:13

score 54 · Answer 8 · 2018-02-01 13:39:06

54

Views

show that every irreducible polynomial on $\mathbb{F}_q[x] $ is separable

Published on 01 Feb 2018 - 13:39

score 37 · Answer 9 · 2026-03-24 22:16:06

37

Views

Show that as roots of an irreducible polynomial in $ \mathbb{F}_q $ are $a,a^q \ldots a^{q^{n-1}}$

Published on 24 Mar 2026 - 22:16

score 67 · Answer 10 · 2018-02-02 10:53:46

67

Views

A sufficient condition for $x^p-x-a$ to be primitive

Published on 02 Feb 2018 - 10:53

score 198 · Answer 11 · 2018-02-02 11:11:35

198

Views

Minimal polynomial of a linear mapping which is semilinear over some extension field

Published on 02 Feb 2018 - 11:11

score 113 · Answer 12 · 2018-02-03 15:26:28

113

Views

Count the number of skew orthogonal matrices over a prime field

Published on 03 Feb 2018 - 15:26

score 1.8k · Answer 13 · 2018-02-03 16:40:05

1.8k

Views

Dimension of vector space generated by finite field over its subfield

Published on 03 Feb 2018 - 16:40

score 453 · Answer 14 · 2026-03-25 02:53:04

453

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For prime $p$, normal subgroups of $SL(2, \mathbb Z/p\mathbb Z)$ remains normal in $GL(2, \mathbb Z/p\mathbb Z)$?

Published on 25 Mar 2026 - 2:53

score 81 · Answer 15 · 2026-03-25 04:34:59

81

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Additive inverses

Published on 25 Mar 2026 - 4:34

List Question

Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$

Period of a binary sequence

Order of $x$ in $\mathbb F_q[x]/(g(x))$

Prove that this quadratically closed extension of $\mathbb{F}_2$ remains quadratically closed after considering cubic extensions

What is the dimension of $\mathbb{R}^2$ over $\mathbb{F}_3$?

How to show that there are no roots of $x^{q+1}+1$ in a finite field of size $q$

Factorization of $x^7 - 1$ into irreducible polynomials over $\Bbb{F_2}[x]$

show that every irreducible polynomial on $\mathbb{F}_q[x] $ is separable

Show that as roots of an irreducible polynomial in $ \mathbb{F}_q $ are $a,a^q \ldots a^{q^{n-1}}$

A sufficient condition for $x^p-x-a$ to be primitive

Minimal polynomial of a linear mapping which is semilinear over some extension field

Count the number of skew orthogonal matrices over a prime field

Dimension of vector space generated by finite field over its subfield

For prime $p$, normal subgroups of $SL(2, \mathbb Z/p\mathbb Z)$ remains normal in $GL(2, \mathbb Z/p\mathbb Z)$?

Additive inverses

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