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 a + b = c {displaystyle a+b=c} has no solution with a , b , c ∈ A {displaystyle a,b,cin A} . 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 a + b = c {displaystyle a+b=c} has no solution with a , b , c ∈ A {displaystyle a,b,cin A} . For example, the set of odd numbers is a sum-free subset of the integers, and the set {N+1, ..., 2N} forms a large sum-free subset of the set {1,...,2N}. 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.