Y by Adventure10, Mango247
For a given positive integer
, let
be the set of all points
in the coordinate plane with
. A point
is called internal if
. A real function
, defined on
, is called good if it has the following property: For every internal point
, the value of
is the arithmetic mean of its values on the four neighboring points (i.e. the points at the distance
from
). Prove that if
and
are good functions that coincide at the non-internal points of
, then
.















