query: Show that $x^n-x-1$ is irreducible over $\mathbb{Z}$
positive_passages.docid: 25471
positive_passages.text: Irreducibility of $x^n-x-1$ over $\mathbb Q$
negative_passages.docid: 146887
negative_passages.text: Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
negative_passages.docid: 114762
negative_passages.text: Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible.
negative_passages.docid: 85459
negative_passages.text: $x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
negative_passages.docid: 65558
negative_passages.text: Irreducible in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 80144
negative_passages.text: Prove that $x-1$ divides $x^n-1$
negative_passages.docid: 26069
negative_passages.text: Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
negative_passages.docid: 102422
negative_passages.text: Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
negative_passages.docid: 76017
negative_passages.text: Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
negative_passages.docid: 90144
negative_passages.text: Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
negative_passages.docid: 41693
negative_passages.text: Use irreducible fibers to show $X$ is irreducible
negative_passages.docid: 109760
negative_passages.text: Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
negative_passages.docid: 46891
negative_passages.text: Irreducibility of reciprocal polynomials
negative_passages.docid: 90612
negative_passages.text: Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
negative_passages.docid: 29545
negative_passages.text: $[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
negative_passages.docid: 116856
negative_passages.text: Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
negative_passages.docid: 133312
negative_passages.text: Are these polynomials irreducible in $\mathbb{Q}[x]$?