2016 IMO Problems/Problem 2
Find all integers for which each cell of
table can be filled with one of the letters
and
in such a way that:
|
Note. The rows and columns of an table are each labelled
to
in a natural order. Thus each cell corresponds to a pair of positive integer
with
. For
, the table has
diagonals of two types. A diagonal of first type consists all cells
for which
is a constant, and the diagonal of this second type consists all cells
for which
is constant.