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) = suma in A \epsilona a, where \epsilona in {0,1} and s(A) = prodn 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)) > C1| A|2 and \omega (s(A)) > C2 \pi (|A|2),

for constants C1 and C2, 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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