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Problem in the "proof" of Eisenstein's criterion on irreducibility.

score 1.4k · Answer 1 · 2026-04-12 01:40:20

1.4k

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Problem in the "proof" of Eisenstein's criterion on irreducibility.

Published on 12 Apr 2026 - 1:40

score 468 · Answer 2 · 2026-04-14 07:38:50

468

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polynomials with same zero set

Published on 14 Apr 2026 - 7:38

score 67 · Answer 3 · 2026-04-14 02:34:24

67

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Proving Polynomial with binomial coefficients

Published on 14 Apr 2026 - 2:34

score 501 · Answer 4 · 2026-04-16 20:52:19

501

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Prove that the irreducible polynomial for $\sqrt2+\sqrt3$ over $\mathbb{Q}$ is reducible modulo $p$ for every prime $p$

Published on 16 Apr 2026 - 20:52

score 797 · Answer 5 · 2026-04-12 04:00:51

797

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Understanding Kronecker's Theorem

Published on 12 Apr 2026 - 4:00

score 346 · Answer 6 · 2026-04-16 18:50:16

346

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Prove that a polynomial of the form $x^p−x−a \in F[x]$ is either irreducible or splits in $F$.

Published on 16 Apr 2026 - 18:50

score 415 · Answer 7 · 2026-04-16 15:15:26

415

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Is $X^p - T$ is irreducible over the separable closure of $\Bbb F_p(T)$?

Published on 16 Apr 2026 - 15:15

score 193 · Answer 8 · 2026-04-15 20:46:14

193

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Will the zeros of linear combination of totally interlacing sequence of polynomials be real?

Published on 15 Apr 2026 - 20:46

score 535 · Answer 9 · 2026-04-14 03:48:33

535

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Factorising polynomials in to their irreducible factors over GF(2)

Published on 14 Apr 2026 - 3:48

score 316 · Answer 10 · 2026-04-16 12:24:35

316

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Isomorphism between two extensions $\Bbb F_2(\alpha)$ and $\Bbb F_2(\beta)$

Published on 16 Apr 2026 - 12:24

score 203 · Answer 11 · 2026-04-15 01:22:18

203

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Prime does not divide index in the ring of integers

Published on 15 Apr 2026 - 1:22

score 65 · Answer 12 · 2026-04-13 03:18:31

65

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Irreducibility of $X^p -p$

Published on 13 Apr 2026 - 3:18

score 61 · Answer 13 · 2026-04-16 00:40:59

61

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Under what conditions is an irreducible polynomial in $\operatorname{GF}(p^m)$ also irreducible in $\operatorname{GF}(p^n)$?

Published on 16 Apr 2026 - 0:40

score 107 · Answer 14 · 2026-04-14 11:48:02

107

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A reducibility of a polynomial $x^2+ax-a+2a^2$

Published on 14 Apr 2026 - 11:48

score 596 · Answer 15 · 2026-04-15 12:36:35

596

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Given degree 3 minimal polynomial of $\alpha$, find minimal polynomial of $\frac{\alpha^2 + \alpha}{2}$

Published on 15 Apr 2026 - 12:36

List Question

Problem in the "proof" of Eisenstein's criterion on irreducibility.

polynomials with same zero set

Proving Polynomial with binomial coefficients

Prove that the irreducible polynomial for $\sqrt2+\sqrt3$ over $\mathbb{Q}$ is reducible modulo $p$ for every prime $p$

Understanding Kronecker's Theorem

Prove that a polynomial of the form $x^p−x−a \in F[x]$ is either irreducible or splits in $F$.

Is $X^p - T$ is irreducible over the separable closure of $\Bbb F_p(T)$?

Will the zeros of linear combination of totally interlacing sequence of polynomials be real?

Factorising polynomials in to their irreducible factors over GF(2)

Isomorphism between two extensions $\Bbb F_2(\alpha)$ and $\Bbb F_2(\beta)$

Prime does not divide index in the ring of integers

Irreducibility of $X^p -p$

Under what conditions is an irreducible polynomial in $\operatorname{GF}(p^m)$ also irreducible in $\operatorname{GF}(p^n)$?

A reducibility of a polynomial $x^2+ax-a+2a^2$

Given degree 3 minimal polynomial of $\alpha$, find minimal polynomial of $\frac{\alpha^2 + \alpha}{2}$

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