List questions from irreducible-polynomials

Published on 06 Nov 2020 - 18:15

110

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If $z \in\mathbb { C } $ is an algebraic integer then $\Pi_z \in\mathbb {Z} [X] $.

Published on 12 Apr 2026 - 4:33

35

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Suppose that Irr($\alpha,\mathbb{Q}$) has odd degree and has one unique real root $\alpha$. Calculate Aut($\mathbb{Q}(\alpha^2)/\mathbb{Q}$)

Published on 08 Nov 2020 - 13:00

189

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Producing a large list of irreducible polynomials of given degree over a specific finite field using a CAS?

Published on 29 Mar 2026 - 3:45

57

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There exist infinitely many prime numbers $p≥2$ and there exist positive integers $k,m$ such that $f(k)=p+m$

Published on 09 Nov 2020 - 17:16

114

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Irreducible polynomial with degree 2 over $\mathbb{R}$

Published on 11 Apr 2026 - 22:30

122

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Irreducibility of integer polynomials

Published on 11 Apr 2026 - 2:43

313

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How to show this polynomial is irreducible over $\mathbb{Q}$?

Published on 14 Nov 2020 - 2:48

328

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Why $0$ is not irreducible?

Published on 11 Apr 2026 - 8:22

546

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Prove $x^4-6x^2+4$ is irreducible

Published on 15 Nov 2020 - 11:03

385

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Why do we study irreducibility of polynomials? What are some real-life applications?

Published on 11 Apr 2026 - 14:31

284

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Factors in unique factorization of multivariate polynomials

Published on 11 Apr 2026 - 2:47

67

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Find irreducible factor of the polynomial

Published on 17 Nov 2020 - 19:42

52

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How to show irreducibility

Published on 08 Apr 2026 - 15:01

249

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Show that $Z^2 + Y^3 + X^5$ is irreducible in $\mathbb C[X,Y,Z].$

Published on 28 Mar 2026 - 23:59

List Question

Check that $\mathbb{Q}[x]/(x^4+1)$ is a field

If $z \in\mathbb { C } $ is an algebraic integer then $\Pi_z \in\mathbb {Z} [X] $.

Suppose that Irr($\alpha,\mathbb{Q}$) has odd degree and has one unique real root $\alpha$. Calculate Aut($\mathbb{Q}(\alpha^2)/\mathbb{Q}$)

Producing a large list of irreducible polynomials of given degree over a specific finite field using a CAS?

There exist infinitely many prime numbers $p≥2$ and there exist positive integers $k,m$ such that $f(k)=p+m$

Irreducible polynomial with degree 2 over $\mathbb{R}$

Irreducibility of integer polynomials

How to show this polynomial is irreducible over $\mathbb{Q}$?

Why $0$ is not irreducible?

Prove $x^4-6x^2+4$ is irreducible

Why do we study irreducibility of polynomials? What are some real-life applications?

Factors in unique factorization of multivariate polynomials

Find irreducible factor of the polynomial

How to show irreducibility

Show that $Z^2 + Y^3 + X^5$ is irreducible in $\mathbb C[X,Y,Z].$

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