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On a Problem of P. Erdös
Published online by Cambridge University Press: 20 November 2018
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P. Erdös asked the following problem: Does there exist an infinite sequence of integers a1<…satisfying for every x≥1
1
so that every integer is of the form 2k+ai [1]. The analogous questions can easily be answered affirmatively if the powers of 2 are replaced by the rth power.
In this note we give a simple affirmative answer to the problem of Erdôs. Let c2 be a sufficiently small absolute constant. Our sequence A consists of all the integers of the form
2
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