query: Factorization in $\mathbb{Z}[\sqrt[4]{3}]$
positive_passages.docid: 148671
positive_passages.text: Trying to factor $x^4-3$ over $\Bbb{F}_p$ with $p\equiv 3\mod{4}$
negative_passages.docid: 52951
negative_passages.text: Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
negative_passages.docid: 99516
negative_passages.text: Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
negative_passages.docid: 47060
negative_passages.text: Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
negative_passages.docid: 44307
negative_passages.text: Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
negative_passages.docid: 53157
negative_passages.text: Factoring Quadratics
negative_passages.docid: 52081
negative_passages.text: Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
negative_passages.docid: 98256
negative_passages.text: Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
negative_passages.docid: 75349
negative_passages.text: Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 67001
negative_passages.text: Factorizing polynomials over fields other than $\mathbb{C}$
negative_passages.docid: 34906
negative_passages.text: Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.
negative_passages.docid: 77903
negative_passages.text: Finding the integral closure of $\mathbb{Z}$ in $\mathbb{Q}[i]$
negative_passages.docid: 153111
negative_passages.text: factoring a quadratic equation
negative_passages.docid: 103763
negative_passages.text: Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$
negative_passages.docid: 113230
negative_passages.text: How can we factor $ q^4 + q^2 + 1$
negative_passages.docid: 61709
negative_passages.text: Compute factor group $\dfrac{\mathbb{Z}_4 \times \mathbb{Z}_6}{\langle(2,3)\rangle}$ - Fraleigh p. 147 Example 15.11