Algebraic number theory is a foundational branch of mathematics that investigates the properties of algebraic numbers and their relationships through the lens of field extensions and rings of integers ...

This is a preview. Log in through your library . Abstract In a quadratic number field $\mathbf{Q}(\sqrt D), D$ a squarefree integer, with class number 1, any algebraic integer can be decomposed ...

A vector $m = (m_1,\ldots, m_n) \in \mathbf{Z}^n\backslash\{0\}$ is called an integer relation for the real numbers $\alpha_1,\ldots, \alpha_n$, if $\sum \alpha_im_i ...

A mathematical proof is a sequence of statements that follow on logically from each other that shows that something is always true. Using letters to stand for numbers means that we can make statements ...