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This conjecture was confirmed by Green and, independently, by Sapozhenko. Here we prove a refined version of their theorem, by showing that the number of sum-free subsets of $[n]$ of size $m$ is $2^{O(n/m)} {\\lceil n/2 \\rceil \\choose m}$, for every $1 \\le m \\le \\lceil n/2 \\rceil$. 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