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'Liouville approximation theorem'
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| Title of object: |
Liouville approximation theorem |
| Canonical Name: |
LiouvillesTheorem |
| Type: |
Theorem |
| Created on: |
2001-10-15 20:20:43-04 |
| Modified on: |
2002-11-07 21:08:50.97905-05 |
| Classification: |
msc:11J68 |
| Keywords: |
number theory |
Revision comment (for changes between this and next version):
| Changes for correction #1404 ('Improvement'). |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic} |
Content:
Given $\alpha$, a real algebraic number of degree $n \neq 1$, there is a constant $c = c( \alpha )$ such that for all rational numbers $p/q, (p,q)=1$, the inequality
\[ \left| \alpha - \frac{p}{q} \right| > \frac{c(\alpha )}{q^n} \] holds. |
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