Publications of (and about) Paul Erdös
Autor: Erdös, Paul
Title: Some applications of graph theory and combinatorial methods to number theory and geometry. (In English)
Source: Algebraic methods in graph theory, Vol. I, Conf. Szeged 1978, Colloq. Math. Soc. Janos Bolyai 25, 137-148 (1981).
Review: [For the entire collection see Zbl 463.00008.]
The paper gives a survey on recent results in some geometric and number-theoretic problemd from the point of view of combinatorial approach. It contains so many results as well as open problems, that we cannot mention all of them here. So we recall only two older (however very interesting) problems: 1. (Corrádi, Erdös, Hajnal) Is it true that if there are given n points in the plane, not all on a line, then they determine at least n-2 different angles? 2. (Erdös, Turán) Let 1 \leq ai \leq ... be an infinite sequence of integers; denote by f(n) the number of solutions of n = ai+aj. If f(n) > 0 for all n > n0, then lim\sup f(n) = oo. P. Erdös offers 500 dollars for a proof or disproof.
Classif.: * 11-02 Research monographs (number theory)
51-02 Research monographs (geometry)
11B83 Special sequences of integers and polynomials
11B75 Combinatorial number theory
Keywords: problems in elementary and combinatorial geometry; applications of graph theory to number theory; survey on recent results
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