IMO 1988 LL GBR20
It is proposed to partition the set of positive integers into two
IMO 1988 LL GBR20
Origin: GBR
Problem
It is proposed to partition the set of positive integers into two disjoint subsets A and B subject to the following conditions: (i) 1 is in A; (ii) no two distinct members of A have a sum of the form 2k + 2 (k = 0, 1, 2, . . .); and (iii) no two distinct members of B have a sum of that form. Show that this partitioning can be carried out in a unique manner and determine the subsets to which 1987, 1988, and 1989 belong.