Problem

Source: India Postal Coaching 2014 Set 1 Problem 5 & Set 4 problem 2

Tags: floor function, number theory, combinatorics unsolved, combinatorics



Let $A=\{1,2,3,\ldots,40\}$. Find the least positive integer $k$ for which it is possible to partition $A$ into $k$ disjoint subsets with the property that if $a,b,c$ (not necessarily distinct) are in the same subset, then $a\ne b+c$.