## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  472.10002
Autor:  Erdös, Paul
Title:  Some problems and results on additive and multiplicative number theory. (In English)
Source:  Analytic number theory, Proc. Conf., Temple Univ./Phila. 1980, Lect. Notes Math. 899, 171-182 (1981).
Review:  [For the entire collection see Zbl 465.00008.]
In this wide-ranging article, the author describes some intriguing problems that have interested him ans others, and he states some old and new conjectures. The first section deals with various questions concerning the divisors of n. The second is concerned with bounds for the greatest k for which the sums ai+aj, where 1 \leq a1 > ... < ak \leq n, are distinct. The final section describes a variety of problems on squarefree integers and similarly constructed sequences, including those on the gaps between consecutive elements, and ends with an interesting theorem on squarefree integers.
Reviewer:  E.J.Scourfield
Classif.:  * 11-02 Research monographs (number theory)
11N05 Distribution of primes
11B83 Special sequences of integers and polynomials
11B75 Combinatorial number theory
00A07 Problem books
Keywords:  problems; divisors and prime factors of integers; additive problems; differences of consecutive primes; sequences defined by divisibility properties; distinct sums; squarefree integers; gaps between consecutive elements
Citations:  Zbl.465.00008

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