List questions from cyclotomic-polynomials

Published on 02 Mar 2016 - 16:40

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Show that $f(x)=q(x)\Phi_p(x)^k$ implies $f(x^2)=r(x)\Phi_p(x)^k$ for some $q,r\in\mathbb{Q}[x]$ with gcd$(q,\Phi_p)=1$, $\gcd(r,\Phi_p)=1$.

Published on 06 Mar 2016 - 12:29

230

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Spotting that $\,x^8 + x^7 + 1\,$ is reducible.

Published on 10 Mar 2016 - 8:56

202

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Compute the minimal polynomial of $u$ over $\Bbb{Q}$ without using cyclotomic polynomials

Published on 11 Mar 2016 - 16:22

312

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solve in positive integers sum of squares of sines equation

Published on 21 Mar 2016 - 1:38

106

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cyclotomic polynomial and unit group

Published on 25 Mar 2016 - 19:57

1.8k

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Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?

Published on 03 Apr 2016 - 11:09

364

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Finding the $18$th cyclotomic polynomial $\phi_{18}(X))$.

Published on 03 Apr 2016 - 16:16

173

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How to design a matrix with multiple chosen eigenvalues?

Published on 03 Apr 2016 - 18:06

478

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Minimal polynomial of root of unity over quadratic field

Published on 25 Mar 2026 - 22:26

64

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Theorem on Repeating Decimals

Published on 11 Apr 2016 - 7:44

806

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Units of $\mathbb Z[X]/(X^n+1)$?

Published on 14 Apr 2016 - 15:16

354

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Irreducibility of special cyclotomic polynomial.

Published on 15 Apr 2016 - 9:52

251

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$\Phi_r\in\mathbb{F}_p[x]$ is the product of $\varphi(r)/a$ irreducible factors of degree $a$

Published on 17 Apr 2016 - 12:09

314

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Prove one of the cyclotomic polynomial identities

Published on 20 Apr 2016 - 15:46

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roots of unity and cyclotomic polynomials over $\mathbb{F}_p$

Show that $f(x)=q(x)\Phi_p(x)^k$ implies $f(x^2)=r(x)\Phi_p(x)^k$ for some $q,r\in\mathbb{Q}[x]$ with gcd$(q,\Phi_p)=1$, $\gcd(r,\Phi_p)=1$.

Spotting that $\,x^8 + x^7 + 1\,$ is reducible.

Compute the minimal polynomial of $u$ over $\Bbb{Q}$ without using cyclotomic polynomials

solve in positive integers sum of squares of sines equation

cyclotomic polynomial and unit group

Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?

Finding the $18$th cyclotomic polynomial $\phi_{18}(X))$.

How to design a matrix with multiple chosen eigenvalues?

Minimal polynomial of root of unity over quadratic field

Theorem on Repeating Decimals

Units of $\mathbb Z[X]/(X^n+1)$?

Irreducibility of special cyclotomic polynomial.

$\Phi_r\in\mathbb{F}_p[x]$ is the product of $\varphi(r)/a$ irreducible factors of degree $a$

Prove one of the cyclotomic polynomial identities

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