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On the probability that n and [n c] are coprime
Authors:Delmer  Francine  Deshouillers  Jean-Marc
Affiliation:(1) A2X, Université Bordeaux 1, 33405 Talence, France;(2) Statistique Mathématique et Applications, Université Victor Segalen, Bordeaux 2, 33076 Bordeaux, France
Abstract:We prove that for any positive real number 
$$c$$
which is not an integer, the density of the integers 
$$n$$
which are coprime to 
$$n^c {text{ is }}6/pi ^2 $$
, a result conjectured by Moser, Lambek and Erd Hs. This revised version was published online in June 2006 with corrections to the Cover Date.
Keywords:distribution modulo 1  greatest common divisor
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