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On a conjecture of Mahler
Published online by Cambridge University Press: 17 April 2009
Abstract
Let R be the field of real numbers. For α in R, let ‖α‖ be the distance of α from the nearest integer. The following conjecture of Kurt Mahler [Bull. Austral. Math. Soc. 14 (1976), 463–465] is proved.
Let m, n be two positive integers n ≥ 2m. Let S be a finite or infinite set of positive integers with the following properties:
(Q1) S contains the integers m, m+1, …, n−m;
(Q2) every element of S satisfies
Then
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 16 , Issue 1 , February 1977 , pp. 125 - 129
- Copyright
- Copyright © Australian Mathematical Society 1977
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