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ON THE ARITHMETIC STRUCTURE OF RATIONAL NUMBERS IN THE CANTOR SET

Part of: Elementary number theory

Published online by Cambridge University Press:  27 April 2020

IGOR E. SHPARLINSKI Open the ORCID record for IGOR E. SHPARLINSKI [Opens in a new window]
IGOR E. SHPARLINSKI*
Affiliation:
Department of Pure Mathematics,University of New South Wales, Sydney, NSW 2052, Australia email igor.shparlinski@unsw.edu.au
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Abstract

We obtain a lower bound on the largest prime factor of the denominator of rational numbers in the Cantor set. This gives a stronger version of a recent result of Schleischitz [‘On intrinsic and extrinsic rational approximation to Cantor sets’, Ergodic Theory Dyn. Syst. to appear] obtained via a different argument.

Keywords

Cantor setdenominators of rational numberslargest prime divisor

MSC classification

Primary: 11A63: Radix representation; digital problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 22 - 27
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This work was supported by ARC Grant DP170100786.

References

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