Hi everyone, let $D$ be a skew field, which is finite dimensional over its center $k$. Assume that $k$ is a number field, and let $\mathcal{O}_D$ be the set of elements $z\in D$ w …

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 in …

Hi, let $k/\mathbb{Q}$ be a number field. Assume that $u$ is an algebraic integer such that all $k$-conjugates have modulus $1$. Is $u$ a root of $1$ ? If $k=\mathbb{Q}$, the ans …

I want to know the exact number of non-negative integer solutions of a1x1+a2x2+...akxk = n ... I know that it is the co-efficient of x^n in (1-x^a1)^-1 * (1-x^a2)^-1 * ... (1-x^ak …

Given a high precision real number, how should I go about guessing an algebraic integer that it's close to? Of course, this is extremely poorly defined -- every real number is clo …