Question

Let $f,g$ be two irreducible polynomials over finite field $\mathbb{F}_q$ such that $\text{ord}(f)=\text{ord}(g)$. Prove that $\deg(f)=\deg(g)$.

score 59 · Answer 1 · 2026-03-22 03:44:09

59

Views

Let $f,g$ be two irreducible polynomials over finite field $\mathbb{F}_q$ such that $\text{ord}(f)=\text{ord}(g)$. Prove that $\deg(f)=\deg(g)$.

Published on 22 Mar 2026 - 3:44

score 124 · Answer 2 · 2026-03-17 19:07:53

124

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Existence of an irreducible trinomial over finite fields?

Published on 17 Mar 2026 - 19:07

score 101 · Answer 3 · 2026-03-17 01:01:49

101

Views

Let $p(x)=x^3-6x-6$

Published on 17 Mar 2026 - 1:01

score 105 · Answer 4 · 2018-01-26 06:25:00

105

Views

How to construct an irreducible polynomial over finite field with a specified order?

Published on 26 Jan 2018 - 6:25

score 47 · Answer 5 · 2018-01-27 06:18:56

47

Views

Does a matrix exist whose eigenpolynomial equals to any polynomial $f(x)$?

Published on 27 Jan 2018 - 6:18

score 824 · Answer 6 · 2026-03-20 06:55:54

824

Views

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

Published on 20 Mar 2026 - 6:55

score 819 · Answer 7 · 2026-03-20 14:06:04

819

Views

Proof verification: The degree of a splitting field of a polynomial $f$ divides deg($f$) factorial

Published on 20 Mar 2026 - 14:06

score 191 · Answer 8 · 2018-01-30 08:10:51

191

Views

Distribution of Irreducible Factors of Polynomials over $\mathbb{F}_2$

Published on 30 Jan 2018 - 8:10

score 106 · Answer 9 · 2026-03-24 16:26:39

106

Views

Irreducibility of $f(x)=x^4+4x-1$

Published on 24 Mar 2026 - 16:26

score 356 · Answer 10 · 2018-02-01 01:54:36

356

Views

How do I know if an ideal $I$ in $\mathbb Z[x]$ is principal? maximal?

Published on 01 Feb 2018 - 1:54

score 1.6k · Answer 11 · 2018-02-01 12:16:35

1.6k

Views

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

Published on 01 Feb 2018 - 12:16

score 1k · Answer 12 · 2018-02-01 20:50:12

1k

Views

Irreducibility of $x^5 - 6x^3 +2x^2 - 4x +5$ in $\mathbb Q[x]$

Published on 01 Feb 2018 - 20:50

score 36 · Answer 13 · 2018-02-02 02:18:17

36

Views

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

Published on 02 Feb 2018 - 2:18

score 52 · Answer 14 · 2018-02-02 20:29:01

52

Views

Adding a prime number to a special homogeneous prime ideal preserves primeness

Published on 02 Feb 2018 - 20:29

score 503 · Answer 15 · 2026-03-17 21:18:45

503

Views

Polynomials: gaining irreducibility by adding a constant

Published on 17 Mar 2026 - 21:18

List Question

Let $f,g$ be two irreducible polynomials over finite field $\mathbb{F}_q$ such that $\text{ord}(f)=\text{ord}(g)$. Prove that $\deg(f)=\deg(g)$.

Existence of an irreducible trinomial over finite fields?

Let $p(x)=x^3-6x-6$

How to construct an irreducible polynomial over finite field with a specified order?

Does a matrix exist whose eigenpolynomial equals to any polynomial $f(x)$?

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

Proof verification: The degree of a splitting field of a polynomial $f$ divides deg($f$) factorial

Distribution of Irreducible Factors of Polynomials over $\mathbb{F}_2$

Irreducibility of $f(x)=x^4+4x-1$

How do I know if an ideal $I$ in $\mathbb Z[x]$ is principal? maximal?

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

Irreducibility of $x^5 - 6x^3 +2x^2 - 4x +5$ in $\mathbb Q[x]$

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

Adding a prime number to a special homogeneous prime ideal preserves primeness

Polynomials: gaining irreducibility by adding a constant

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