Tag Archives: sum-free

2016-7 Sum-free

For a set \( A \subset \mathbb{R} \), let \( f(A) \) be the size of the largest set \( B \subset A \) such that \( (B+B) \cap B = \emptyset \). For a positive integer \( n \), let \( f(n) = \min_{0 \notin A, |A|=n} f(A) \). Prove that \( f(n) \geq n/3 \).

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