query: Prove that : $x^n+4$ is irreducible in $\mathbb{Z}[x]$.
positive_passages.docid: 10627
positive_passages.text: When is $X^n-a$ is irreducible over F?
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: 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: 157031
negative_passages.text: Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$
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: 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: 134726
negative_passages.text: Show the polynomial is irreducible in $\textbf Z_2$
negative_passages.docid: 143107
negative_passages.text: Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?
negative_passages.docid: 19968
negative_passages.text: Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.
negative_passages.docid: 125604
negative_passages.text: Proof that $\mathbb{Z}$ has no zero divisors
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: 31215
negative_passages.text: Irreducible cyclotomic polynomial
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: 113359
negative_passages.text: Proving that $x^2 + 4$ is not divisible by $3$
negative_passages.docid: 138275
negative_passages.text: Show $100+t$ is reducible in $\mathbb{Z}[[t]]$
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: 26069
negative_passages.text: Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?