MathDB

In a plane we choose a cartesian system of coordinates. A point

A(x,y)

in the plane is called an integer point if and only if both

x

and

y

are integers. An integer point

A

is called invisible if on the segment

(OA)

there is at least one integer point. Prove that for each positive integer

n

there exists a square of side

n

in which all the interior integer points are invisible.

Problem Statement