Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  715.11014
Autor:  Erdös, Paul; Zaks, Abraham
Title:  Reducible sums and splittable sets. (In English)
Source:  J. Number Theory 36, No.1, 89-94 (1990).
Review:  For ai,ni in N, i = 1,...,k set s = sumki = 1ai/ni. If s' = sumki = 1ai'/ni, 0 \leq ai' \leq ai, then s' is called a subsum of s. Further, s is called reducible if a subsum s' = 1 exists. The set {n1,...,nk} is called splittable iff whenever s is an integer greater than 1, then s is reducible. - In the paper criteria for reducibility and examples of irreducible sums are given. Further, relations between nonsplittable sets and irreducible sums are studied.
Reviewer:  St.Znám
Classif.:  * 11B99 Sequences and sets
Keywords:  reducible sums; splittable sets; sum of fractions of positive integers

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