Abstract
Let p be a prime. A set A of residues modulo p is said to be sum-free if there are no solutions to a = a′ + a″ with a, a′, a″ ∈ A. We show that there are 2p/3+o(p) such sets. We also count the number of distinct sets of the form B + B, where B is a set of residues modulo p. Once again, there are 2p/3+o(p) such sets.
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