$d$-complete sequences of integers
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- by P. Erdos and Mordechai Lewin PDF
- Math. Comp. 65 (1996), 837-840 Request permission
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
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- 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), 111β124. MR 130236
- P. ErdΕs, Quickie, Math. Mag. 67 (1994), pp. 67 and 74.
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
- Received by editor(s): January 30, 1994
- Received by editor(s) in revised form: August 3, 1994, February 12, 1995, and March 16, 1995
- © Copyright 1996 American Mathematical Society
- 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