Problem

Source: China TST 2011 - Quiz 2 - D1 - P2

Tags: calculus, derivative, function, algebra, polynomial, modular arithmetic, combinatorics unsolved



Let be a positive integer, and let m,n be positive integers with mn, such that A1,A2,,Am,B1,,Bm are m+n pairwise distinct subsets of the set {1,2,,}. It is known that AiΔBj are pairwise distinct, 1im,1jn, and runs over all nonempty subsets of {1,2,,}. Find all possible values of m,n.