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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
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Abstract

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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