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**Zentralblatt MATH**

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

**Zbl.No: ** 144.28103

**Autor: ** Erdös, Pál

**Title: ** Extremal problems in number theory (In English)

**Source: ** Proc. Sympos. Pure Math. 8, 181-189 (1965).

**Review: ** Several problems are discussed of which the following are typical examples;

1. Determine the maximum number of integers not exceeding n, no k of which form an arithmetic progression.

2. Is the maximum number of integers not exceeding n from which one cannot select k+1 integers which are pairwise relatively prime equal to the number of integers not exceeding n which are multiples of at least one of the first k primes?

3. Let f(n; a_{1},...,a_{k}) be the number of solutions of n = **sum**_{i = 1}^{k} \epsilon_{i} a_{i},\epsilon_{i} = 0 or 1 where the a_{i} are k distinct real numbers. Is **max**_{n,a1,...,ak} f(n,a_{1},...,a_{k}) < c {2^{k} \over k^{3/2}}?

**Reviewer: ** R.C.Entringer

**Classif.: ** * 11B75 Combinatorial number theory

11B25 Arithmetic progressions

**Index Words: ** number theory

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag