On a Problem of P. Erdös

Abstract

P. Erdös asked the following problem: Does there exist an infinite sequence of integers a 1 <…satisfying for every x≥1 1 so that every integer is of the form 2 k +a i [1]. The analogous questions can easily be answered affirmatively if the powers of 2 are replaced by the r th power. In this note we give a simple affirmative answer to the problem of Erdôs. Let c 2 be a sufficiently small absolute constant. Our sequence A consists of all the integers of the form 2

Locations

• Canadian Mathematical Bulletin - View - PDF