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**Zentralblatt MATH**

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

**Zbl.No: ** 445.10002

**Autor: ** Erdös, Paul

**Title: ** Nine little known problems in combinatorial number theory. (In NO)

**Source: ** Normat 1980, 155-164 (1980).

**Review: ** In this paper the author discusses various problems in combinatorial number theory. We mention some examples. In \S1 the following is discussed: Is there a partition of the naturals into k subsets for some k such that the sum of two distinct elements from the same subset is never a square. The next paragraphs discuss problems related to sequences of natural numbers, density questions, and functions related to these sequences. The last paragraph is devoted to primes, espectially the behaviour of p_{i+1}-p_{i}, p_{i} the i-th prime, and related functions is discussed.

**Reviewer: ** R.Rudolph

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

11P81 Elementary theory of partitions

11B05 Topology etc. of sets of numbers

11B13 Additive bases

11B83 Special sequences of integers and polynomials

11B25 Arithmetic progressions

11N05 Distribution of primes

11N37 Asymptotic results on arithmetic functions

00A07 Problem books

**Keywords: ** problems in combinatorial number theory; partition of naturals; sequences; density questions; difference of consecutive primes

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