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