- #1
- 5,665
- 1,567
A set A of non-zero integers is called sum-free if for all choices of [itex] a,b\in A[/itex], a+b is not contained in A.
The Challenge: Find a constant c > 0 such that for every finite set of integers B not containing 0, there is a subset A of B such that A is sum-free and |A| ≥ c|B|, where |A| means the number of elements of A.Every solution (by a new poster) which improves on the best constant known up until that point in the thread will be awarded a fresh 2 points, and of course alternate solutions which do not improve on the best known constant are more than welcome as well! Solutions which show a c exists but do not calculate it are also OK.
The Challenge: Find a constant c > 0 such that for every finite set of integers B not containing 0, there is a subset A of B such that A is sum-free and |A| ≥ c|B|, where |A| means the number of elements of A.Every solution (by a new poster) which improves on the best constant known up until that point in the thread will be awarded a fresh 2 points, and of course alternate solutions which do not improve on the best known constant are more than welcome as well! Solutions which show a c exists but do not calculate it are also OK.
Last edited: