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The Quarterly Journal of Mathematics Advance Access published online on December 4, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham051
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© 2007. Published by Oxford University Press. All rights reserved For permissions, please email: journals.permissions@oxfordjournals.org

SIMULTANEOUS DIOPHANTINE APPROXIMATION BY SQUARE-FREE NUMBERS

Rainer Dietmann{dagger}

Institut für Algebra und Zahlentheorie, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

{dagger} E-mail: dietmarr{at}mathematik.uni-stuttgart.de

Received 20 April 2007;
  Abstract

Let {alpha}1, ...,{alpha}r isin R be ‘not very well approximable’, for example, Q-linearly independent real algebraic numbers. Then there are infinitely many positive square-free integers n such that Formula, where ||·|| denotes distance to the nearest integer.


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