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Remarks on a Problem of Obreanu

Published online by Cambridge University Press:  20 November 2018

P. Erdös  and
A. Rényi
P. Erdös
Affiliation:
University College London, England
A. Rényi
Affiliation:
University College London, England
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Let a1 < a2 < … be any sequence of integers. Assume that the infinite sequence of numbers un satisfies the following condition: To every ɛ > 0 there is an no = no (ɛ) such that for all n > no and all k

1

Obreanu asked (Problem P. 35 Can. Math. Bull.) under what conditions on the sequence a1 < a2 < … does (1) imply that the sequence u is convergent. N. G. de Bruijn and P. Erdos proved that a necessary and sufficient condition for (1) to imply the convergence of un is that the sequence {an} be infinite and that the greatest common divisor of the a1 should be 1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 6 , Issue 2 , May 1963 , pp. 267 - 273
Copyright
Copyright © Canadian Mathematical Society 1963