On the probability that n and [nc] are coprime

Francine Delmer; Jean-Marc Deshouillers

doi:10.1023/a:1022337727769

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 45: Issue 1-2

On the probability that n and [n^c] are coprime

Authors: Francine Delmer¹ and Jean-Marc Deshouillers²

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¹ A2X Université Bordeaux 1 33405 Talence France Université Bordeaux 1 33405 Talence France
² Université Victor Segalen Statistique Mathématique et Applications Bordeaux 2 33076 Bordeaux France Bordeaux 2 33076 Bordeaux France

DOI:: https://doi.org/10.1023/a:1022337727769

Page Count:: 15–20

Publication Date:: 01 Sep 2002

Online Publication Date:: 03 Jan 2005

Article Category:: Research Article

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Abstract

We prove that for any positive real number

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$c$$ \end{document}

which is not an integer, the density of the integers

which are coprime to

, a result conjectured by Moser, Lambek and Erd Hs.