query: When are the integers extended with the nth root of unity a unique factorization domain?
positive_passages.docid: 153664
positive_passages.text: When is $\Bbb{Z[\zeta_n]}$ a PID?
negative_passages.docid: 134352
negative_passages.text: The number of possible factorizations of a positive integer.
negative_passages.docid: 69935
negative_passages.text: Field extensions of finite degree and primitive elements
negative_passages.docid: 93291
negative_passages.text: Method for determining irreducibles and factorising in $\mathbb Z[\sqrt{d}]$
negative_passages.docid: 7891
negative_passages.text: Sum of nth roots of unity
negative_passages.docid: 89473
negative_passages.text: Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
negative_passages.docid: 135152
negative_passages.text: Non-UFD integral domain such that prime is equivalent to irreducible?
negative_passages.docid: 128550
negative_passages.text: Algebraic field extension and intermediate integral domain
negative_passages.docid: 66272
negative_passages.text: Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
negative_passages.docid: 74024
negative_passages.text: Higher dimensional equivalent of complex numbers
negative_passages.docid: 121404
negative_passages.text: How to factor polynomials in $\mathbb{Z}_n$?
negative_passages.docid: 58717
negative_passages.text: Why isn't $\mathbb Z [\sqrt{pq}]$ a factorial domain
negative_passages.docid: 14827
negative_passages.text: RSA: Fast factorization of N if d and e are known
negative_passages.docid: 102914
negative_passages.text: Integral domain that is not a factorization domain
negative_passages.docid: 93820
negative_passages.text: Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
negative_passages.docid: 56985
negative_passages.text: Show that every positive integer has a unique representation in the form $50k+l$...?
negative_passages.docid: 134699
negative_passages.text: Can *any* real polynomial be factored linearly (plus a constant) over $\mathbb{R}$?