It is proposed to partition a set of positive integers into two disjoint subsets A and B subject to the conditions
i.) 1 is in A
ii.) no two distinct members of A have a sum of the form 2^k \plus{} 2, k \equal{} 0,1,2, \ldots; and
iii.) no two distinct members of B have a sum of that form.
Show that this partitioning can be carried out in unique manner and determine the subsets to which 1987, 1988 and 1989 belong. combinatorics unsolvedcombinatorics