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A distance problem of P. Erdős with some further restrictions

✍ Scribed by Ilona Palásti

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
129 KB
Volume
76
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Here we have an example for six points in the plane no three on a line no four on a circle, and no one equidistant from three others, such that they determine 5 distinct distances, one occurring once, one twice, one three times, one four times, and one five times, and the configuration does not contain equilateral triangles.

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In this paper we shall answer a question of Erd6s and Graham (1980, p. 18) concerning sums of integer sequences. Furthermore, we shall examine for what sequences (ri, ci)~l it is true that if B = (bi) is a sequence of natural numbers such bi+l >~ribi -c~ then, for some sequence A = (ai)~=l of natura