The Structure of Maximum Subsets of $\{1,\ldots,n\}$ with No Solutions to $a+b = kc$

  • Andreas Baltz
  • Peter Hegarty
  • Jonas Knape
  • Urban Larsson
  • Tomasz Schoen

Abstract

If $k$ is a positive integer, we say that a set $A$ of positive integers is $k$-sum-free if there do not exist $a,b,c$ in $A$ such that $a + b = kc$. In particular we give a precise characterization of the structure of maximum sized $k$-sum-free sets in $\{1,\ldots,n\}$ for $k\ge 4$ and $n$ large.

Published
2005-04-28
Article Number
R19