Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T05:12:25.698Z Has data issue: false hasContentIssue false
  • English
  • Français

The Integers as Differences of a Sequence

Published online by Cambridge University Press:  20 November 2018

Andrew Pollington  and
Charles Vanden Eynden
Andrew Pollington
Affiliation:
Department of Mathematics, Illinois State University, Normal, Illinois 61761
Charles Vanden Eynden
Affiliation:
Department of Mathematics, Illinois State University, Normal, Illinois 61761
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that there exists a sequence of integers a1 < a2 <... such that each positive integer is a difference of elements of the sequence in exactly one way, and such that ak does not exceed a constant times k3. In fact we construct such a sequence with each ak in [C(k -1)3, Ck3), where C is an absolute constant.

Keywords

10L99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 497 - 499
Copyright
Copyright © Canadian Mathematical Society 1981

References

Problem, P. 290, this Bulletin, Vol. 23, No. 3, 1980 and 24 (4), 1981, 504-505 (this issue).Google Scholar