Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  448.10002
Autor:  Erdös, Paul
Title:  A survey of problems in combinatorial number theory. (In English)
Source:  Ann. Discrete Math. 6, 89-115 (1980).
Review:  Problems are presented in the following areas: the theorem of van der Waerden and Szemerédi; covering congruences, additive number theory, dense sets of integers, infinite subsets of integers (related to the work of Hindmann), sieve methods and other miscellaneous topics. An attempt is made to describe what has happened to problems mentioned in previous surveys. Some old conjectures still remain open, for example the following one of 45 years standing: if 1 \leq a1 < ... < ak \leq x is a sequence of integers such that the sums sum1k\epsiloniai, \epsiloni = 0or1, are all different, then max k = \frac{log x}{log 2}+0(1). 500 dollars is coffered for its solution. A larger survey due to the author and R. L. Graham can be found in ''Old and new problems and results in combinatorial number theory'' [L'Enseignment Math., Monographie 28 (1980; Zbl 434.10001)].
Reviewer:  I.Anderson
Classif.:  * 11-02 Research monographs (number theory)
                   11B25 Arithmetic progressions
                   11B83 Special sequences of integers and polynomials
                   11P32 Additive questions involving primes
                   11N05 Distribution of primes
                   11A99 Elementary number theory
                   00A07 Problem books
                   05A05 Combinatorial choice problems
Keywords:  problems; covering congruences; dense sets of integers; infinite subsets of integers; sieve methods
Citations:  Zbl.434.10001

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