Erdős Problem #748
Cameron-Erdős conjecture

Let \(f(n)\) count the number of sum-free \(A\subseteq \{1,\ldots,n\}\), i.e. \(A\) contains no solutions to \(a=b+c\) with \(a,b,c\in A\). Is it true that \[f(n)=2^{(1+o(1))\frac{n}{2}}?\] The Cameron–Erdős conjecture. This is true, and in fact \(f(n) \ll 2^{n/2}\), which was proved independently by Green [Gr04] and Sapozhenko [Sa03]. The statement \(f(n)=2^{(1+o(1))n/2}\) is formalised as \(\log_2 f(n)/n\to 1/2\).