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On the fractional parts of the powers of a rational number (II)

Published online by Cambridge University Press:  26 February 2010

K. Mahler
K. Mahler
Affiliation:
The University, Manchester 13.
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Extract

About twenty years ago, in a note of the same title [2], I obtained the following result.

THEOREM 1. Let u and v be relatively prime integers satisfying u> v ≥ 2 and let ε be an arbitrarily small positive number. Suppose the inequality

is satisfied by an infinite sequence of positive integers n1 n2, … Then

Information

Type
Research Article
Information
Mathematika , Volume 4 , Issue 2 , December 1957 , pp. 122 - 124
Copyright
Copyright © University College London 1957

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References

1.Hardy, G. H. and Wright, E. M., Introduction to the Theory of Numbers (3rd ed., Oxford, 1954).Google Scholar
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