Question

Irreducible factors of $X^p-1$ in $(\mathbb{Z}/q \mathbb{Z})[X]$

score 1.9k · Answer 1 · 2026-04-12 13:22:13

1.9k

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Irreducible factors of $X^p-1$ in $(\mathbb{Z}/q \mathbb{Z})[X]$

Published on 12 Apr 2026 - 13:22

score 541 · Answer 2 · 2026-04-13 20:07:30

541

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Irreducible polynomial not attaining squares over finite field

Published on 13 Apr 2026 - 20:07

score 343 · Answer 3 · 2026-04-14 21:03:50

343

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Polynomial over characteristic two finite field of odd degree with certain image

Published on 14 Apr 2026 - 21:03

score 1k · Answer 4 · 2026-04-13 19:07:23

1k

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$f(x)$ is irreducible if and only if $f(x)$ does not have a root in $\mathbb{Z}/\mathbb{2Z}.$

Published on 13 Apr 2026 - 19:07

score 6.7k · Answer 5 · 2026-04-14 06:28:20

6.7k

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Explicit construction of a finite field with $8$ elements

Published on 14 Apr 2026 - 6:28

score 519 · Answer 6 · 2026-04-16 23:48:15

519

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When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?

Published on 16 Apr 2026 - 23:48

score 834 · Answer 7 · 2026-04-13 03:11:53

834

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Proof for latin squares- disjoint transversals

Published on 13 Apr 2026 - 3:11

score 665 · Answer 8 · 2026-04-16 16:58:19

665

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A pair of MOLS of order 15?

Published on 16 Apr 2026 - 16:58

score 5.4k · Answer 9 · 2026-04-14 17:07:46

5.4k

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Why is the product of all units of a finite field equal to $-1$?

Published on 14 Apr 2026 - 17:07

score 2.5k · Answer 10 · 2026-04-12 12:12:09

2.5k

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The Frobenius endomorphism

Published on 12 Apr 2026 - 12:12

score 2.7k · Answer 11 · 2026-04-16 15:40:34

2.7k

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Number of irreducible polynomials with degree $6$ in $\mathbb{F}_2[X]$

Published on 16 Apr 2026 - 15:40

score 1.7k · Answer 12 · 2026-04-11 21:26:23

1.7k

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If two polynomials are equal as functions, are they necessarily equal as polynomials?

Published on 11 Apr 2026 - 21:26

score 1.9k · Answer 13 · 2026-04-16 15:19:51

1.9k

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Whats the probability a subset of an $\mathbb F_2$ vector space is a spanning set?

Published on 16 Apr 2026 - 15:19

score 319 · Answer 14 · 2026-04-18 07:49:49

319

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Proving that if $\mathrm{char}(F)=p>0$ then if $g(x)\in F[x]$ is irreducible then $g(x)$ have multiple roots iff $g'(x)=0$

Published on 18 Apr 2026 - 7:49

score 358 · Answer 15 · 2026-04-16 19:14:48

358

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For which values of $n$ is the polynomial $p(x)=1+x+x^2+\cdots+x^n$ irreducible over $\mathbb{F}_2[x]$?

Published on 16 Apr 2026 - 19:14

List Question

Irreducible factors of $X^p-1$ in $(\mathbb{Z}/q \mathbb{Z})[X]$

Irreducible polynomial not attaining squares over finite field

Polynomial over characteristic two finite field of odd degree with certain image

$f(x)$ is irreducible if and only if $f(x)$ does not have a root in $\mathbb{Z}/\mathbb{2Z}.$

Explicit construction of a finite field with $8$ elements

When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?

Proof for latin squares- disjoint transversals

A pair of MOLS of order 15?

Why is the product of all units of a finite field equal to $-1$?

The Frobenius endomorphism

Number of irreducible polynomials with degree $6$ in $\mathbb{F}_2[X]$

If two polynomials are equal as functions, are they necessarily equal as polynomials?

Whats the probability a subset of an $\mathbb F_2$ vector space is a spanning set?

Proving that if $\mathrm{char}(F)=p>0$ then if $g(x)\in F[x]$ is irreducible then $g(x)$ have multiple roots iff $g'(x)=0$

For which values of $n$ is the polynomial $p(x)=1+x+x^2+\cdots+x^n$ irreducible over $\mathbb{F}_2[x]$?

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