Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  216.32201
Autor:  Erdös, Paul; Straus, E.G.
Title:  Some number theoretic results (In English)
Source:  Pac. J. Math. 36, 635-646 (1971).
Review:  The paper consists of two disconnected parts. In the first part the authors investigate the maximal number f(p) of residues mod p so that sums of different number of distinct elements of our set are distinct mod p. They prove

(4p)1/3+o(p1/3) < f(p) < (288p)1/3+o(p1/3).

It is conjectured that the lower bound gives the correct order of magnitude. In the second part they investigate the irrationality of series of the form

sum oon = 1{un \over a1,a2 ... an},a1 \leq a2 \leq ... .


Classif.:  * 11J72 Irrationality
                   11B83 Special sequences of integers and polynomials
                   05D05 Extremal set theory

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