## 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; a1,...,ak) be the number of solutions of n = sumi = 1k \epsiloni ai,\epsiloni = 0 or 1 where the ai are k distinct real numbers. Is maxn,a1,...,ak f(n,a1,...,ak) < c {2k \over k3/2}?
Reviewer:  R.C.Entringer
Classif.:  * 11B75 Combinatorial number theory
11B25 Arithmetic progressions
Index Words:  number theory

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