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Mathematics of Computation

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$d$-complete sequences of integers


Authors: P. Erdos and Mordechai Lewin
Journal: Math. Comp. 65 (1996), 837-840
MSC (1991): Primary 11B13
DOI: https://doi.org/10.1090/S0025-5718-96-00707-7
MathSciNet review: 1333312
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Abstract | References | Similar Articles | Additional Information

Abstract: An infinite sequence $a_1<a_2<\dotsb$ is $d$-complete if every sufficiently large integer is the sum of $a_i$ such that no one divides the other. We investigate $d$-completeness of sets of the form $\{p^\alpha q^\beta\}$ and $\{p^\alpha q^\beta r^\gamma\}$ with $\alpha,\beta,\gamma$ nonnegative.


References [Enhancements On Off] (What's this?)

  • 1. B. J. Birch, On 3𝑁 points in a plane, Proc. Cambridge Philos. Soc. 55 (1959), 289–293. MR 0109315
  • 2. J. W. S. Cassels, On the representation of integers as the sums of distinct summands taken from a fixed set, Acta Sci. Math. Szeged 21 (1960), 111–124. MR 0130236
  • 3. P. Erd\H{o}s, Quickie, Math. Mag. 67 (1994), pp. 67 and 74.

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Additional Information

P. Erdos
Affiliation: Mathematical Institute, Hungarian Academy of Sciences, Realtanoda u. 13-15, H-1053 Budapest, Hungary and Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel

Mordechai Lewin
Affiliation: Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel
Email: mole@techunix.technion.ac.il

DOI: https://doi.org/10.1090/S0025-5718-96-00707-7
Received by editor(s): January 30, 1994
Received by editor(s) in revised form: August 3, 1994, February 12, 1995, and March 16, 1995
Article copyright: © Copyright 1996 American Mathematical Society