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A theorem on diophantine approximations

Published online by Cambridge University Press:  17 April 2009

Kurt Mahler
Kurt Mahler
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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If S is a set of positive integers which contains 1, 2, …, n–1, but not n or any multiple of n, where n ≥ 2, then

Here R is the field of real numbers, and ∥α∥ denotes the distance of α from the nearest integer.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 463 - 465
Copyright
Copyright © Australian Mathematical Society 1976