Longest convex lattice chains

Let T   be a triangle with two specified vertices v0,v1∈Z2v0,v1∈Z2. A convex lattice chain in T   from v0v0 to v1v1 is defined naturally (see the next paragraph). In this paper we prove what the maximal length of a convex lattice chain is if the area of T is fixed (and large). It is also shown that the solution is unique apart from lattice preserving affine transformations.