A lattice point in the coordinate plane with origin O is called invisible if the segment OA contains a lattice point other than O and A. Let L be a positive integer. Show that there exists a square with side length L and sides parallel to the coordinate axes, such that all points in the square are invisible.

(In reply to

some progress by Steven Lord)

Having taken time to read the problem and do some digging, I believe the intent of this problem is to generalize on

The invisible square: http://perplexus.info/show.php?pid=1211

My interpretation is that 'The invisible square' is the L=1 subcase of this problem and the goal is to show there are arbitrarily large squares of lattice points such all the points are invisible.