List questions from irreducible-polynomials

Published on 25 Mar 2026 - 11:15

237

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The polynomial $x^{2k} + 1 + (x+1)^{2k}$ is not divisible by $x^2 + x +1$. Find value of $k$ such that it belongs to natural numbers.

Published on 20 Feb 2020 - 12:18

189

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Polynomial rings and quotients of homogeneous ideals

Published on 26 Mar 2026 - 11:04

88

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Resolving $x^6-x^4-1=0$ (only interested in $x\simeq1.21$)

Published on 21 Feb 2020 - 12:38

46

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Galois Field Polynomial Exponentiation

Published on 25 Feb 2020 - 20:48

105

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Process for checking reducibility of polynomials of degree 2 or lower in $\mathbb{Z}_2$

Published on 26 Feb 2020 - 4:33

155

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How to use Chinese Remainder Theorem

Published on 28 Mar 2026 - 22:30

170

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Show that $f(x)$ is irreducible

Published on 28 Feb 2020 - 2:46

60

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Product of Roots

Published on 28 Feb 2020 - 5:11

109

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Prove p(x) is not a primitive polynomial

Published on 28 Feb 2020 - 18:02

227

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If $N$ is large enough, then $x^5-Nx+1$ and $x^5-Nx^2+1$ are irreducible over $\mathbb{Q}$.

Published on 29 Feb 2020 - 10:45

271

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Does $-1$ have a square root in the ring $\frac{\mathbb R[x]}{\langle(x^2+1)^2\rangle}$?

Published on 02 Mar 2020 - 9:28

471

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Showing that the fifteenth cyclotomic polynomial is ireducible over $\mathbb{Q}$

Published on 26 Mar 2026 - 9:41

95

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Minimum polynomial of the $11^{\text{th}}$ root of unity

Published on 26 Mar 2026 - 11:08

221

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is the polynomial $\ x^3 - y^5$ irreducible in $\ \Bbb Q[x, y]$

Published on 05 Mar 2020 - 12:44

List Question

Is $f$ irreducible in $\mathbb Z[x], \mathbb Q [x], \mathbb Z[i][x], \mathbb Q [i][x]$

The polynomial $x^{2k} + 1 + (x+1)^{2k}$ is not divisible by $x^2 + x +1$. Find value of $k$ such that it belongs to natural numbers.

Polynomial rings and quotients of homogeneous ideals

Resolving $x^6-x^4-1=0$ (only interested in $x\simeq1.21$)

Galois Field Polynomial Exponentiation

Process for checking reducibility of polynomials of degree 2 or lower in $\mathbb{Z}_2$

How to use Chinese Remainder Theorem

Show that $f(x)$ is irreducible

Product of Roots

Prove p(x) is not a primitive polynomial

If $N$ is large enough, then $x^5-Nx+1$ and $x^5-Nx^2+1$ are irreducible over $\mathbb{Q}$.

Does $-1$ have a square root in the ring $\frac{\mathbb R[x]}{\langle(x^2+1)^2\rangle}$?

Showing that the fifteenth cyclotomic polynomial is ireducible over $\mathbb{Q}$

Minimum polynomial of the $11^{\text{th}}$ root of unity

is the polynomial $\ x^3 - y^5$ irreducible in $\ \Bbb Q[x, y]$

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