Combinatorial Problems in Geometry and Number Theory

In a previous paper (given at the International Congress of Mathematicians at Nice 1970) entitled "On the application of combinatorial analysis to number theory geometry and analysis", I discussed many combinatorial results and their applications . I will refer to this paper as I (as much as possible I will try to avoid overlap with this paper) . First I discuss those problems mentioned in I where significant progress has been made . 1 . Let f(n) be the smallest integer so that if there are f(n) points in the plane no three on a line, then there are always n of them which form the vertices of a convex n-gon . was discussed in I . Szekeres and I proved that 2n-4 (1) 2n-2 + 1 s f(n) 5 n-2 This problem of E . Klein (Mrs Szekeres)