Question

If $f$ has $\deg(f)$ distince roots whose order are the same, then is $f$ irreducible?

score 85 · Answer 1 · 2026-05-04 21:52:22

85

Views

If $f$ has $\deg(f)$ distince roots whose order are the same, then is $f$ irreducible?

Published on 04 May 2026 - 21:52

score 244 · Answer 2 · 2026-04-29 12:47:05

244

Views

Counting squares in finite fields (Paley Design)

Published on 29 Apr 2026 - 12:47

score 81 · Answer 3 · 2026-04-29 12:46:58

81

Views

Is $g\mid f$ and $ord(f)=ord(g)$ implies that the splitting field of $f$ equals that of $g$?

Published on 29 Apr 2026 - 12:46

score 548 · Answer 4 · 2026-04-29 12:47:08

548

Views

Is my proof that finite fields have order $p^n$ valid?

Published on 29 Apr 2026 - 12:47

score 62 · Answer 5 · 2026-05-04 23:51:26

62

Views

Characterize ideals in $\mathbb{F}_l[x]/(x-1) \oplus \mathbb{F}_l[x]/(\frac{x^p-1}{x-1})$

Published on 04 May 2026 - 23:51

score 103 · Answer 6 · 2026-04-29 12:47:08

103

Views

help me to understand this part of the book on finite fields

Published on 29 Apr 2026 - 12:47

score 151 · Answer 7 · 2026-05-07 18:58:56

151

Views

How do I manually compute the point doubling of the point (3, 6) on the curve $y^2 = x^3 + 2x + 3$?

Published on 07 May 2026 - 18:58

score 280 · Answer 8 · 2026-05-02 05:16:23

280

Views

Why is $\mathbb{Q}(\sqrt{2})$ not isomorphic to $\mathbb{Q}(\sqrt{3})$?

Published on 02 May 2026 - 5:16

score 72 · Answer 9 · 2026-05-03 20:06:36

72

Views

Question on quadratic forms of dimension 3

Published on 03 May 2026 - 20:06

score 223 · Answer 10 · 2026-04-17 00:13:07

223

Views

Is $\phi: \mathbb{F_p}(X) \rightarrow \mathbb{F_p}(X), a \mapsto a$ for $a \in \mathbb{F_p}$ and $X \mapsto X+1$ a field homomorphism?

Published on 17 Apr 2026 - 0:13

score 66 · Answer 11 · 2026-04-29 12:24:23

66

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 29 Apr 2026 - 12:24

score 1.6k · Answer 12 · 2026-04-29 12:47:04

1.6k

Views

Does the field with 27 elements contain a subfield with 9 elements?

Published on 29 Apr 2026 - 12:47

score 31 · Answer 13 · 2026-04-29 12:47:00

31

Views

What is the expected difference in the gap of two polynomials in $Z_2[x_1, ..., x_n]$ when adding a randomly chosen variable $x_i, i \in [n]$?

Published on 29 Apr 2026 - 12:47

score 110 · Answer 14 · 2026-04-29 12:47:08

110

Views

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

Published on 29 Apr 2026 - 12:47

score 49 · Answer 15 · 2026-04-29 12:47:15

49

Views

Regarding some field notation

Published on 29 Apr 2026 - 12:47

List Question

If $f$ has $\deg(f)$ distince roots whose order are the same, then is $f$ irreducible?

Counting squares in finite fields (Paley Design)

Is $g\mid f$ and $ord(f)=ord(g)$ implies that the splitting field of $f$ equals that of $g$?

Is my proof that finite fields have order $p^n$ valid?

Characterize ideals in $\mathbb{F}_l[x]/(x-1) \oplus \mathbb{F}_l[x]/(\frac{x^p-1}{x-1})$

help me to understand this part of the book on finite fields

How do I manually compute the point doubling of the point (3, 6) on the curve $y^2 = x^3 + 2x + 3$?

Why is $\mathbb{Q}(\sqrt{2})$ not isomorphic to $\mathbb{Q}(\sqrt{3})$?

Question on quadratic forms of dimension 3

Is $\phi: \mathbb{F_p}(X) \rightarrow \mathbb{F_p}(X), a \mapsto a$ for $a \in \mathbb{F_p}$ and $X \mapsto X+1$ a field homomorphism?

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

Does the field with 27 elements contain a subfield with 9 elements?

What is the expected difference in the gap of two polynomials in $Z_2[x_1, ..., x_n]$ when adding a randomly chosen variable $x_i, i \in [n]$?

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

Regarding some field notation

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