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On Some Diophantine Inequalities Involving the Exponential Function

Published online by Cambridge University Press:  20 November 2018

A. Baker
A. Baker*
Affiliation:
Trinity College, Cambridge, England
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It is well known that for any real number θ there are infinitely many positive integers n such that

Here ||a|| denotes the distance of a from the nearest integer, taken positively. Indeed, since ||a|| < 1, this implies more generally that if θ1, θ2, . . . , θk are any real numbers, then there are infinitely many positive integers n such that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 616 - 626
Copyright
Copyright © Canadian Mathematical Society 1965

References

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