Abstract
A set A of integers is called sum-free if a + b ∉ A for any a , b ∈ A . For any real numbers q ≤ p we denote by [ q , p ] the set of real numbers x such that q ≤ x ≤ p . Let S ( t , n ) stand for the family of all sum-free subsets A ⊆ [ t , n ], and s ( t , n ) = | S ( t , n )|. We prove that s ( t , n ) = O (2 n /2 ) for t ≥ n 3/4 log n , where log t = log 2 t .
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