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Multiplicative properties of sets of residues. (English) Zbl 1287.11043

Summary: Given a natural number \(n\), we ask whether every set of residues mod \(n\) of cardinality at least \(n/2\) contains elements \(a, b, c\) with \(ab = c\). It is proved that the set of numbers \(n\) failing to have this property has upper density smaller than \(1.56 \times 10^{-8}\).

MSC:

11B75 Other combinatorial number theory
11B05 Density, gaps, topology
20D05 Finite simple groups and their classification
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