The Cameron–Erdős conjecture

A subset AA of integers is said to be sum-free   if a+b∉Aa+b∉A for any a,b∈Aa,b∈A. Let s(n)s(n) be the number of sum-free sets in interval [1,n][1,n] of integers. P. Cameron and P. Erdős conjectured that s(n)=O(2n/2)s(n)=O(2n/2). We show that s(n)∼c^02n/2 for even n   and s(n)∼c^12n/2 for odd n  , where c^0,c^1 are absolute constants, thereby proving the conjecture.