1997 IMO Problems/Problem 1
Problem
In the plane the points with integer coordinates are the vertices of unit squares. The squares are colored alternatively black and white (as on a chessboard).
For any pair of positive integers and
, consider a right-angled triangle whose vertices have integer coordinates and whose legs, of lengths
and
, lie along edges of the squares.
Let be the total area of the black part of the triangle and
be the total area of the white part.
Let
(a) Calculate for all positive integers
and
which are either both even or both odd.
(b) Prove that for all
and
.
(c) Show that there is no constant such that
for all
and
.
Solution
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