## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  061.07302
Autor:  Erdös, Pál
Title:  On a problem of Sidon in additive number theory and on some related problems. Addendum. (In English)
Source:  J. London Math. Soc. 19, 208 (1944).
Review:  For a given positive integer n the authors consider sets of distinct positive integers a1,a2,...,ar not exceeding n such that the sums ai+aj (1 \leq i \leq j \leq r) are all different. Let \Phi(n) denote the maximum value which r can have for any such set. Then \Phi(n) denote the maximum value which r can have for any such set. Then \Phi(n) < n ½+2n1/4 for any n. On the other hand, if n = p2k+pk+1, where k is a positive integer and p is a prime, then \Phi(n) > n ½ (cf. J.Singer, Zbl 019.00502).
Reviewer:  P.T.Bateman
Classif.:  * 11B34 Representation functions
Index Words:  number theory

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