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Erdős problem 866

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Estimate the least excess gk(N)g_k(N) forcing kk integers whose pairwise sums all lie in a dense subset of {1,…,2N}\{1, \dots, 2N\}; in particular, determine the positive variant h4(n)h_4(n).

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Estimate the least excess $g_k(N)$ forcing $k$ integers whose pairwise sums all lie in a dense subset of $\{1, \dots, 2N\}$; in particular, determine the positive variant $h_4(n)$.

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