query: Show that the polynomial $x^2+y^2-1$ is irreducible over $\mathbb{Q}[x,y]$
positive_passages.docid: 94579
positive_passages.text: $\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
negative_passages.docid: 148909
negative_passages.text: Irreducible polynomials of degree 3 and 5
negative_passages.docid: 134726
negative_passages.text: Show the polynomial is irreducible in $\textbf Z_2$
negative_passages.docid: 91356
negative_passages.text: Irreducibility of an infinite sequence of polynomials
negative_passages.docid: 46891
negative_passages.text: Irreducibility of reciprocal polynomials
negative_passages.docid: 24626
negative_passages.text: Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
negative_passages.docid: 70581
negative_passages.text: Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$?
negative_passages.docid: 38364
negative_passages.text: Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
negative_passages.docid: 26069
negative_passages.text: Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
negative_passages.docid: 120147
negative_passages.text: For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
negative_passages.docid: 51952
negative_passages.text: Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
negative_passages.docid: 53669
negative_passages.text: Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
negative_passages.docid: 53012
negative_passages.text: Irreducibility of a polynomial if it has no root (Capelli)
negative_passages.docid: 121714
negative_passages.text: Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
negative_passages.docid: 79564
negative_passages.text: Algorithm to find the irreducible polynomial
negative_passages.docid: 8977
negative_passages.text: Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible