MathDB

2

Part of 2001 Baltic Way

Problems(1)

Each expressible as n integers from different sets

Source: Baltic Way 2001

11/17/2010
Let n≥2n\ge 2 be a positive integer. Find whether there exist nn pairwise nonintersecting nonempty subsets of {1,2,3,…}\{1, 2, 3, \ldots \} such that each positive integer can be expressed in a unique way as a sum of at most nn integers, all from different subsets.
arithmetic sequencecombinatorics proposedcombinatorics