query: On the irreducibility of the polynomial $x^{n}−\alpha$
positive_passages.docid: 10627
positive_passages.text: When is $X^n-a$ is irreducible over F?
negative_passages.docid: 8977
negative_passages.text: Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible
negative_passages.docid: 133312
negative_passages.text: Are these polynomials irreducible in $\mathbb{Q}[x]$?
negative_passages.docid: 156671
negative_passages.text: Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
negative_passages.docid: 118916
negative_passages.text: How do I prove that a polynomial F[x] of degree n has at most n roots
negative_passages.docid: 48268
negative_passages.text: How many $\alpha \in S_n$ are such that $\alpha^2 = 1$?
negative_passages.docid: 27942
negative_passages.text: showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
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: 63605
negative_passages.text: Irreducible polynomials and affine variety
negative_passages.docid: 151961
negative_passages.text: Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
negative_passages.docid: 64878
negative_passages.text: Is this polynomial irreducible in $\mathbb{Q}$?
negative_passages.docid: 54192
negative_passages.text: Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
negative_passages.docid: 154373
negative_passages.text: How many irreducible monic quadratic polynomials are there in $\mathbb{F}_p[X]$?
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: 108385
negative_passages.text: Irreducible factors of $x^8 - x$ in $Z/2Z[x]$
negative_passages.docid: 140808
negative_passages.text: Problem on Galois theory and irreducible polynomial
negative_passages.docid: 74777
negative_passages.text: Solvability and reducibility of a polynomial in a "chain" of finite fields