Accession Number : AD0619219

Title :   ON THE REPRESENTATION OF INTERGERS AS SUMS OF DISTINCT TERMS FROM A FIXED SEQUENCE,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Folkman,Jon

Report Date : AUG 1965

Pagination or Media Count : 32

Abstract : Consideration is given a problem that has received considerable attention recently. Let a sub 1, a sub 2, a sub 3, . . . be a sequence of positive integers. If every sufficiently large integer can be represented as a sum of distinct terms from this sequence, one says that the sequence is complete. The general problem is: Characterize complete sequences. This memorandum considers this problem for the class of sequences which are either increasing with a sub n = 0(n alpha) or strictly increasing with a sub n = 0(n 1+alpha), where 0 < alpha < 1. It shows that a necessary and sufficient condition for such a sequence to be complete is that at least one term from every infinite arithmetic progression should be representable as a sum of distinct terms from the sequence. (Author)

Descriptors :   (*NUMBER THEORY, SEQUENCES(MATHEMATICS)), NUMERICAL ANALYSIS, SERIES(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE