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PROBLEM #863Let r\geq 2 and let A\subseteq \{1,\ldots,N\} be a set of maximal size such that there are at most r solutions to n=a+b with a\leq b for any n. (That is, A is a B_2[r] set.)Similarly, let B\subseteq \{1,\ldots,N\} be a set of maximal size such that there are at most r solutions to n=a-b for any n\geq 1. If \lvert A\rvert\sim c_rN^{1/2} as N\to \infty and \lvert B\rvert \sim c_r'N^{1/2} as N\to \infty then is it true that c_r\neq c_r' for r\geq 2? Is it true that c_r'<c_r?1930OPEN ↗

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