Abstract
According to an old result of Turán, any ( n + 1)-subset of {1, 2, ..., 2 n } contains a pair of divisible numbers. Ciurea et al. have recently considered a natural algorithmic variant of this classic mathematical result: if the subset is not known, and it is only accessible via a membership oracle, what is the minimum number of questions necessary to identify one such divisible pair? They showed a 4/3 n -- O (1) lower bound and also designed an algorithm which they conjectured asks no more than 4/3 n + O (1) queries, and therefore would be optimal. We reanalyze the proposed algorithm and prove that it comes close to the conjectured value, in asking no more than (4/3 + 5/108) n + O (1) queries; this corrects an error in the old analysis.
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