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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 ], ands  ( t ,  n ) = | S  ( t ,  n )|.

On the number and structure of sum-free sets in a segment of positive integers