Question

Finding all polynomials $f(X), g(X)\in \mathbb{F}_5[X]$ such that $f(X)\neq g(X)$ and $f(x)=g(x)\neq 0$ for $x\in\mathbb{F_5}$.

score 39 · Answer 1 · 2020-11-29 16:18:48

39

Views

Finding all polynomials $f(X), g(X)\in \mathbb{F}_5[X]$ such that $f(X)\neq g(X)$ and $f(x)=g(x)\neq 0$ for $x\in\mathbb{F_5}$.

Published on 29 Nov 2020 - 16:18

score 267 · Answer 2 · 2020-11-29 23:36:11

267

Views

What are the irreducible elements of the polynomial ring $\mathbb Q[x]$?

Published on 29 Nov 2020 - 23:36

score 636 · Answer 3 · 2020-12-01 01:30:41

636

Views

Factoring $x^{n}-1$ over the finite field $\mathbf F_q$.

Published on 01 Dec 2020 - 1:30

score 74 · Answer 4 · 2020-12-01 02:16:28

74

Views

Reducible and irreducible polynomials

Published on 01 Dec 2020 - 2:16

score 48 · Answer 5 · 2020-12-01 03:56:45

48

Views

Irreducible and reducible polynomial

Published on 01 Dec 2020 - 3:56

score 46 · Answer 6 · 2020-12-03 20:42:49

46

Views

Prove a necessary condition for the irreducibility of a polynomial over F_p

Published on 03 Dec 2020 - 20:42

score 70 · Answer 7 · 2020-12-05 13:34:59

70

Views

Determine if the polynomial f(x) = $2x^5 + 5x^4 + 4x^3 + 7x^2 + 7x + 2$ is reducible to $\mathbb Q $

Published on 05 Dec 2020 - 13:34

score 141 · Answer 8 · 2020-12-06 19:57:02

141

Views

To Show that, $f$ cannot be expressed as the product of two polynomials with integer coefficients and degree $>1.$

Published on 06 Dec 2020 - 19:57

score 151 · Answer 9 · 2026-03-30 02:07:51

151

Views

Norm of a polynomial $N_{E/K}(f)(X)$ with $E/K$ a Galois extension

Published on 30 Mar 2026 - 2:07

score 84 · Answer 10 · 2020-12-08 20:06:15

84

Views

No polynomials of degree > 0 are such that $p(t)^2 + q(t)^2 =1$

Published on 08 Dec 2020 - 20:06

score 908 · Answer 11 · 2020-12-10 18:11:48

908

Views

Prove that $\sqrt{3} + \sqrt{7}$ is a primitive element of $\mathbb{Q}(\sqrt{3},\sqrt{7})$

Published on 10 Dec 2020 - 18:11

score 54 · Answer 12 · 2020-12-11 10:21:26

54

Views

How to prove irreducibility of $P(x)=x^4-2x^3-2x^2+2x-1$ over $\mathbb{Q}$?

Published on 11 Dec 2020 - 10:21

score 284 · Answer 13 · 2020-12-11 22:27:53

284

Views

If $n>1$, are there $f_1,\dots,f_k\in\mathbb{Z}[x]$ of degree $n$ such that, for any prime $p$, some $f_i$ is irreducible and of degree $n$, mod $p$?

Published on 11 Dec 2020 - 22:27

score 114 · Answer 14 · 2026-03-29 10:49:12

114

Views

Find polynomials $r(x)$ and $s(x)$ such that $r(x)(x^2+x+1)+s(x)(x^3-x-1)=1$.

Published on 29 Mar 2026 - 10:49

score 31 · Answer 15 · 2026-04-11 17:54:22

31

Views

Roots of $PQ$ if $Q$ is irreducible + Condition on degree?

Published on 11 Apr 2026 - 17:54

List Question

Finding all polynomials $f(X), g(X)\in \mathbb{F}_5[X]$ such that $f(X)\neq g(X)$ and $f(x)=g(x)\neq 0$ for $x\in\mathbb{F_5}$.

What are the irreducible elements of the polynomial ring $\mathbb Q[x]$?

Factoring $x^{n}-1$ over the finite field $\mathbf F_q$.

Reducible and irreducible polynomials

Irreducible and reducible polynomial

Prove a necessary condition for the irreducibility of a polynomial over F_p

Determine if the polynomial f(x) = $2x^5 + 5x^4 + 4x^3 + 7x^2 + 7x + 2$ is reducible to $\mathbb Q $

To Show that, $f$ cannot be expressed as the product of two polynomials with integer coefficients and degree $>1.$

Norm of a polynomial $N_{E/K}(f)(X)$ with $E/K$ a Galois extension

No polynomials of degree > 0 are such that $p(t)^2 + q(t)^2 =1$

Prove that $\sqrt{3} + \sqrt{7}$ is a primitive element of $\mathbb{Q}(\sqrt{3},\sqrt{7})$

How to prove irreducibility of $P(x)=x^4-2x^3-2x^2+2x-1$ over $\mathbb{Q}$?

If $n>1$, are there $f_1,\dots,f_k\in\mathbb{Z}[x]$ of degree $n$ such that, for any prime $p$, some $f_i$ is irreducible and of degree $n$, mod $p$?

Find polynomials $r(x)$ and $s(x)$ such that $r(x)(x^2+x+1)+s(x)(x^3-x-1)=1$.

Roots of $PQ$ if $Q$ is irreducible + Condition on degree?

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