query: Prove that $ x^4 - 2 $ is irreducible over $ \mathbb{Z}[i] $
positive_passages.docid: 24626
positive_passages.text: Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
negative_passages.docid: 1487
negative_passages.text: How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
negative_passages.docid: 70249
negative_passages.text: Irreducibility of Polynomials in $k[x,y]$
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: 2043
negative_passages.text: $X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
negative_passages.docid: 41693
negative_passages.text: Use irreducible fibers to show $X$ is irreducible
negative_passages.docid: 46292
negative_passages.text: Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
negative_passages.docid: 51221
negative_passages.text: Is $x^3-9$ irreducible over the integers mod 31?
negative_passages.docid: 78143
negative_passages.text: Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
negative_passages.docid: 157031
negative_passages.text: Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$
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: 22632
negative_passages.text: Galois group of $x^4-2$
negative_passages.docid: 37068
negative_passages.text: How could it possible to factorise $x^8-1$ in product of irreducibles in the rings $(\mathbb{Z}/2\mathbb{Z})[x]$ and $(\mathbb{Z}/3\mathbb{Z})[x]$?
negative_passages.docid: 146887
negative_passages.text: Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
negative_passages.docid: 96087
negative_passages.text: Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?
negative_passages.docid: 27577
negative_passages.text: An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
negative_passages.docid: 10627
negative_passages.text: When is $X^n-a$ is irreducible over F?