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**Zentralblatt MATH**

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

**Zbl.No: ** 434.10001

**Autor: ** Erdös, Paul; Graham, Ronald L.

**Title: ** Old and new problems and results in combinatorial number theory. (In English)

**Source: ** Monographie No.28 de L'Enseignement Mathématique. Genève: L'Enseignement Mathématique, Université de Genève. 128 p. (1980).

**Review: ** This survey of open problems contains chapters on each of the following topics: van der Warden's theorem and related topics, covering congruences, unit fractions, bases, completeness of sequences, irrationality and transcendence, diophantine problems, miscellaneous problems. There then follows ten pages of remarks on an earlier similar paper [*P. Erdös*, ibid. 6, 81-135 (1963; Zbl 117.02901)] , bringing that survey up to date. A full bibliography, and an author index of over 300 names, are also included. Fascinating to dip into.

**Reviewer: ** I.Anderson

**Classif.: ** * 11-02 Research monographs (number theory)

00A07 Problem books

**Keywords: ** combinatorial number theory; arithmetic progression; survey of open problems; van der Waerden's theorem; covering congruences; unit fractions; bases; completeness of sequences; irrationality and transcendence; diophantine problems

**Citations: ** Zbl.117.029

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag