×

Old and new problems and results in combinatorial number theory. (English) Zbl 0434.10001

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 follow ten pages of remarks on an earlier similar paper [P. Erdős, ibid. 6, 81–135 (1963; Zbl 0117.02901)], bringing that survey up to date. A full bibliography, and an author index of over 300 names, are also included. Fascinating to dip into.

MSC:

11-02 Research exposition (monographs, survey articles) pertaining to number theory
00A07 Problem books
11A07 Congruences; primitive roots; residue systems
11B25 Arithmetic progressions
11B75 Other combinatorial number theory
11B83 Special sequences and polynomials
11D68 Rational numbers as sums of fractions
11J72 Irrationality; linear independence over a field
11J81 Transcendence (general theory)

Citations:

Zbl 0117.02901