In this paper we prove that if
is
the square of a prime and
is
a set of
points
determining at least
directions, then either
is
affinely equivalent to the graph of the function
or it determines
at least
directions. This is sharp, the example is due to Polverino, Szőnyi and Weiner.
Our method combines the lacunary polynomial and the double power sum
approach.
Keywords
affine planes, directions, blocking sets of Rédei type