We want to split the set of natural numbers from 1 to 3n, where n is a natural number, into n mutually disjoint sets {x,y,z} of three elements such that always holds: x+y=3z. Is this possible for :
a) n=5?
b) n=10?
In both cases, provide either such a split or proof that such a split is not possible. number theorycombinatorics