# Tagged Questions

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### Cyclotomic integers with given modulus

The following problem was posted to the NMBRTHRY mailing list about a week ago, without eventually getting a satisfactory solution.
Suppose that $p=(n^2+1)/2$ is a prime, with $n\ge 5$ integer. Does ...

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**1**answer

337 views

### is there any bound on the absolute number of algebraic integer in terms of its degree?

If Z is a sum of t distinct roots of unity and |Z| is a rational integer, can someone find a bound on |Z| in terms of k=deg(Q(Z):Q))?
Clearly we need to have distinct roots of unity otherwise this ...

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**1**answer

401 views

### When does the modulus of a sum of an integer and an algebraic integer equal an integer?

Let say Z is a sum of n-roots of unity and thus an algebraic integer, and D is an rational integer.
If |z+D| is an integer, what can we conclude regarding Z? can we say |Z| is integer?
Another ...

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**3**answers

764 views

### which algebraic integers in a cyclotomic field give you integer absolute value?

Does anyone know an answer to this question?
Question: In an cyclotomic field which algebraic integers have integer absolute value?
Revision 1: -1
I like to add this to the above question, Let's ...

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### Ring of algebraic integers in a quadratic extension of a cyclotomic field

Hello,
I have a question which arose when trying to classify orders of certain algebras.
We know that if $K=\mathbb{Q}(\zeta)$ is any cyclotomic field, and $\zeta$ is an $n$-th root of unity (for ...