  R. B. Kusner [R. Guy, Amer. Math. Monthly 90 (1983), 196--199] asked whether
a set of vectors in a d-dimensional real vector space such that the l-p
distance between any pair is 1, has cardinality at most d+1. We show that this
is true for p=4 and any d >= 1, and false for all 1<p<2 with d sufficiently
large, depending on p.
  More generally we show that the maximum cardinality is at most $(2\lceil
p/4\rceil-1)d+1$ if p is an even integer, and at least $(1+\epsilon_p)d$ if
1<p<2, where $\epsilon_p>0$ depends on p.
