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On the Representation of Integers as Sums of Distinct Terms from a Fixed Sequence

Published online by Cambridge University Press:  20 November 2018

Jon Folkman
Jon Folkman*
Affiliation:
The Rand Corporation, Santa Monica, California
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Let A = (a1, a2, a3, …) be a sequence of positive integers. We let

denote the set of integers that are sums of distinct terms of A. If P(A) contains all sufficiently large integers, we say that A is complete. We shall show that certain classes of sequences that are characterized by their rate of growth are complete.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 643 - 655
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Cassels, J. W. S., On the representation of integers as sums of distinct summands taken from a fixed set, Acta Szeged., 21 (1960), 111–124.Google Scholar
2. Erdös, P., On the representation of large integers as sums of distinct summands taken from a fixed set, Acta Arith., 7 (1962), 345–354.Google Scholar