Sum-free set
In additive combinatorics and number theory, a subset A of an abelian group G is said to be sum-free if the sumset A⊕A is disjoint from A. In other words, A is sum-free if the equation has no solution with.
For example, the set of odd numbers is a sum-free subset of the integers, and the set forms a large sum-free subset of the set. Fermat's Last Theorem is the statement that, for a given integer n > 2, the set of all nonzero nth powers of the integers is a sum-free subset.
Some basic questions that have been asked about sum-free sets are:
A sum-free set is said to be maximal if it is not a proper subset of another sum-free set.
