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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 841.11048

**Autor: ** Erdös, Paul; Sárközy, A.; Stewart, C.L.

**Title: ** On prime factors of subset sums. (In English)

**Source: ** J. Lond. Math. Soc., II. Ser. 49, No.2, 209-218 (1994).

**Review: ** As usual, \omega(n) denotes the number of distinct prime factors of n and P(n) denotes the largest prime factor of n. Further, for any finite non-empty set A of positive integers S(A) = **sum**_{a in A} \epsilon_{a} a, where \epsilon_{a} in **{**0,1**}** and s(A) = **prod**_{n in S(A)} n. This paper is about the behaviour of P(s (A))/ |A| and \omega (s(A))/ \pi(|A|) as the cardinality | A| of A increases without bound. The authors conjecture that P(s (A)) > C_{1}| A|^{2} and \omega (s(A)) > C_{2} \pi (|A|^{2}), for constants C_{1} and C_{2}, and they obtain several results in which they prove these conjectures under certain explicit density restrictions imposed on A.

**Reviewer: ** R.J.Stroeker (Rotterdam)

**Classif.: ** * 11N35 Sieves

11N25 Distribution of integers with specified multiplicative constraints

11B83 Special sequences of integers and polynomials

**Keywords: ** prime factors of subset sums; sieves

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