Question 50
in a plan endowed with a coordinate system $X O Y$ A point is called a lattice $A(x, y)$ where both coordinates are integers. a lattice point $A$ It is called invisible if in the open segment $O A$ There is at least one lattice point. Show that for any natural number $n$, $n \gt 0$, there is a side square $n$ where all the inner lattic points, on the sides or in the tips, are invisible.