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minimum overlap problem : ウィキペディア英語版 | minimum overlap problem In number theory, the minimum overlap problem is a problem proposed by Hungarian mathematician Paul Erdős in 1955. == Formal statement of the problem ==
Let and be two complementary subsets, a splitting of the set of natural numbers , such that both have the same cardinality, namely . Denote by the number of solutions of the equation , where is an integer varying between . is defined as: : The problem is to estimate when is sufficiently large.〔
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