@article {MATHEDUC.02310942,
author = {Beck, I. and Bejlegaard, N. and Erd\"os P. and Fishburn, P.},
title = {Equal distance sums in the plane.},
year = {1995},
journal = {Normat},
volume = {43},
number = {4},
issn = {0801-3500},
pages = {150-161},
publisher = {Nationellt Centrum f\"or Matematikutbildning (NCM), G\"oteborgs Universitet, G\"oteborg},
abstract = {An equisum set in the plane is a finite set X$_n$ of distinct points $\lbrack{}$x$_1, x_2$, ..., $x_n\rbrack{}$ such that the sum of the distances from x$_i$ to all of the other points in X is the same for all i = 1, 2, ..., n. The authors show that an equisum set in which all the interpoint distances are different must have at least 5 elements. They also investigate the possible numbers of different interpoint distances in an equisum set with 5 elements.},
msc2010 = {G45xx},
identifier = {1996a.00451},
}