0
votes
1answer
118 views

Aurifeuillean factorization with number fields

Basically the question is if number fields can be used in Aurifeuillean factorization. Probably this is easy and the answer is "no". Let $f,g \in \mathbb{Z}[x], a \in \mathbb{N}$. Let $f(x)$ and ...
7
votes
2answers
317 views

Number of ways to write an integer as a product of irreducibles

Is there any way to tell the number of distinct ways to factor $a\in\mathcal{O}_k$ (up to units, of course) when $k$ is not a PID? A simple investigation in $\mathbb{Q}(\sqrt{-5})$ with integer ring ...
2
votes
1answer
641 views

A subring question (revised)

Hello, Let $K/{\mathbb Q}$ be a finite extension which is not necessarily Galois, and ${\mathcal O}$ be the ring of integers of $K$. Let $p$ be a prime in ${\mathbb Q}$ and let $p {\mathcal ...