query: Is $x^n - y^m$ irreducible ($n, m$ strictly positive integers with $n \ne m$)?
positive_passages.docid: 156671
positive_passages.text: Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
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: 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: 93291
negative_passages.text: Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
negative_passages.docid: 8164
negative_passages.text: Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
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: 106914
negative_passages.text: Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
negative_passages.docid: 20612
negative_passages.text: Is fibre product of varieties irreducible (integral)?
negative_passages.docid: 25290
negative_passages.text: Determine the number of irreducible monic polynomials of degree 3 in $\mathbb F_p[x]$
negative_passages.docid: 25471
negative_passages.text: Irreducibility of $x^n-x-1$ over $\mathbb Q$
negative_passages.docid: 111935
negative_passages.text: Irreducible but not prime
negative_passages.docid: 10821
negative_passages.text: Using Eisenstein criterion show that $x^3+x^2-2x-1$ is irreducible?
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field
negative_passages.docid: 6943
negative_passages.text: Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$
negative_passages.docid: 40114
negative_passages.text: Factor into irreducibles in $\mathbb{Z}[\omega]$ (Eisenstein Integers).
negative_passages.docid: 46951
negative_passages.text: For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
negative_passages.docid: 91356
negative_passages.text: Irreducibility of an infinite sequence of polynomials