Good sets and coloring of all positive integers.
Source: Moldova 2008 IMO-BMO Third TST Problem 4
March 30, 2008
searchfloor functioncombinatorics proposedcombinatorics
Problem Statement
A non-empty set of positive integers is said to be good if there is a coloring with colors of all positive integers so that no number in is the sum of two different positive integers (not necessarily in ) of the same color. Find the largest value can take so that the set S\equal{}\{a\plus{}1,a\plus{}2,a\plus{}3,\ldots,a\plus{}t\} is good, for any positive integer .
[hide="P.S."]I have the feeling that I've seen this problem before, so if I'm right, maybe someone can post some links...