Question

$P,R \neq 0$ are polynomials with rational coefficients. Show that there exists a polynomial $Q$ such that $P(X) | Q(R(X))$

score 152 · Answer 1 · 2020-05-30 22:56:45

152

Views

$P,R \neq 0$ are polynomials with rational coefficients. Show that there exists a polynomial $Q$ such that $P(X) | Q(R(X))$

Published on 30 May 2020 - 22:56

score 144 · Answer 2 · 2020-05-31 00:50:01

144

Views

Finding irreducible polynomial in finite field

Published on 31 May 2020 - 0:50

score 353 · Answer 3 · 2020-05-31 04:25:54

353

Views

Prove polynomial is irreducible in $Z_p[x]$.

Published on 31 May 2020 - 4:25

score 36 · Answer 4 · 2020-05-31 18:47:39

36

Views

Let $F=\Bbb{F}_3[x]/(f(x))$ and $\alpha=x+f(x) \Bbb{F}_3 \in F$, so that $f(\alpha)=0$ Prove that f(x) is irreducible

Published on 31 May 2020 - 18:47

score 61 · Answer 5 · 2026-03-26 16:06:20

61

Views

Differences between polynomial quotient rings $\mathbb{Z}_m[x]/(x^n+1)$ and $\mathbb{Z}_m[x]/(x^n-1)$

Published on 26 Mar 2026 - 16:06

score 238 · Answer 6 · 2020-06-01 19:31:18

238

Views

How can I prove that a polynomial is irreducible over $\mathbb Z[x]$?

Published on 01 Jun 2020 - 19:31

score 21 · Answer 7 · 2020-06-02 17:48:27

21

Views

Irreducibility of Polynomials over Residue Class Ring

Published on 02 Jun 2020 - 17:48

score 147 · Answer 8 · 2020-06-02 18:36:55

147

Views

List all monic irreducible polynomials of prime degree $p$ over $\mathbb{F}_p$

Published on 02 Jun 2020 - 18:36

score 59 · Answer 9 · 2026-03-28 16:44:39

59

Views

A problem regarding polynomials with only prime powers

Published on 28 Mar 2026 - 16:44

score 223 · Answer 10 · 2020-06-04 12:47:23

223

Views

Specific detail in the irreducibility of $(x-1)(x-2)...(x-n)-1$ in the integers.

Published on 04 Jun 2020 - 12:47

score 34 · Answer 11 · 2026-03-26 21:12:26

34

Views

Find splitting field and irreducible decomposition

Published on 26 Mar 2026 - 21:12

score 100 · Answer 12 · 2020-06-08 18:53:58

100

Views

Irreducible polynomial in field extension (alternative proof)

Published on 08 Jun 2020 - 18:53

score 21 · Answer 13 · 2020-06-09 22:28:24

21

Views

Question about generator of $K[x]$ using simple extension.

Published on 09 Jun 2020 - 22:28

score 62 · Answer 14 · 2020-06-09 22:37:14

62

Views

Is the following a correct proof that $t^4-32$ is irreducible over $\mathbb{Z}$?

Published on 09 Jun 2020 - 22:37

score 75 · Answer 15 · 2020-06-10 08:20:45

75

Views

When the polynomial $16(n+1)^2(p(x)-1)^3p(x)+1$ is a perfect square

Published on 10 Jun 2020 - 8:20

List Question

$P,R \neq 0$ are polynomials with rational coefficients. Show that there exists a polynomial $Q$ such that $P(X) | Q(R(X))$

Finding irreducible polynomial in finite field

Prove polynomial is irreducible in $Z_p[x]$.

Let $F=\Bbb{F}_3[x]/(f(x))$ and $\alpha=x+f(x) \Bbb{F}_3 \in F$, so that $f(\alpha)=0$ Prove that f(x) is irreducible

Differences between polynomial quotient rings $\mathbb{Z}_m[x]/(x^n+1)$ and $\mathbb{Z}_m[x]/(x^n-1)$

How can I prove that a polynomial is irreducible over $\mathbb Z[x]$?

Irreducibility of Polynomials over Residue Class Ring

List all monic irreducible polynomials of prime degree $p$ over $\mathbb{F}_p$

A problem regarding polynomials with only prime powers

Specific detail in the irreducibility of $(x-1)(x-2)...(x-n)-1$ in the integers.

Find splitting field and irreducible decomposition

Irreducible polynomial in field extension (alternative proof)

Question about generator of $K[x]$ using simple extension.

Is the following a correct proof that $t^4-32$ is irreducible over $\mathbb{Z}$?

When the polynomial $16(n+1)^2(p(x)-1)^3p(x)+1$ is a perfect square

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