Question

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

score 77 · Answer 1 · 2026-03-22 10:22:14

77

Views

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

Published on 22 Mar 2026 - 10:22

score 238 · Answer 2 · 2026-03-22 17:00:58

238

Views

Counting squares in finite fields (Paley Design)

Published on 22 Mar 2026 - 17:00

score 77 · Answer 3 · 2018-01-21 06:56:57

77

Views

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

Published on 21 Jan 2018 - 6:56

score 542 · Answer 4 · 2026-03-17 18:11:37

542

Views

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

Published on 17 Mar 2026 - 18:11

score 55 · Answer 5 · 2026-03-17 09:28:27

55

Views

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

Published on 17 Mar 2026 - 9:28

score 97 · Answer 6 · 2026-03-17 15:51:29

97

Views

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

Published on 17 Mar 2026 - 15:51

score 142 · Answer 7 · 2026-03-19 22:03:41

142

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 19 Mar 2026 - 22:03

score 270 · Answer 8 · 2026-03-24 20:47:47

270

Views

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

Published on 24 Mar 2026 - 20:47

score 65 · Answer 9 · 2026-03-22 10:05:12

65

Views

Question on quadratic forms of dimension 3

Published on 22 Mar 2026 - 10:05

score 221 · Answer 10 · 2026-03-24 23:49:54

221

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 24 Mar 2026 - 23:49

score 59 · Answer 11 · 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 1.6k · Answer 12 · 2026-03-24 23:42:55

1.6k

Views

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

Published on 24 Mar 2026 - 23:42

score 27 · Answer 13 · 2018-01-25 19:52:39

27

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 25 Jan 2018 - 19:52

score 106 · Answer 14 · 2026-03-24 22:12:58

106

Views

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

Published on 24 Mar 2026 - 22:12

score 43 · Answer 15 · 2026-03-16 23:27:42

43

Views

Regarding some field notation

Published on 16 Mar 2026 - 23:27

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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