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**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 a_{i},n_{i} in **N**, i = 1,...,k set s = **sum**^{k}_{i = 1}a_{i}/n_{i}. If s' = **sum**^{k}_{i = 1}a_{i}'/n_{i}, 0 \leq a_{i}' \leq a_{i}, then s' is called a subsum of s. Further, s is called reducible if a subsum s' = 1 exists. The set **{**n_{1},...,n_{k}**}** 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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