Pomerance, Carl; Schinzel, Andrzej Multiplicative properties of sets of residues. (English) Zbl 1287.11043 Mosc. J. Comb. Number Theory 1, No. 1, 52-66 (2011). 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 \(1.56 \times 10^{-8}\). Cited in 1 Review MSC: 11B75 Other combinatorial number theory 11B05 Density, gaps, topology 20D05 Finite simple groups and their classification Keywords:product-free sets PDFBibTeX XMLCite \textit{C. Pomerance} and \textit{A. Schinzel}, Mosc. J. Comb. Number Theory 1, No. 1, 52--66 (2011; Zbl 1287.11043) Full Text: Link Online Encyclopedia of Integer Sequences: Decimal expansion of Sum_{p} 1/(p^2-1), summed over the primes p = A000040. Numbers having exactly one non-unitary prime factor. Decimal expansion of the upper asymptotic density of certain sets of residues. Decimal expansion of eta_2, a constant related to the asymptotic density of certain sets of residues. Decimal expansion of eta_3, a constant related to the asymptotic density of certain sets of residues. Decimal expansion of eta_4, a constant related to the asymptotic density of certain sets of residues. Decimal expansion of eta_5, a constant related to the asymptotic density of certain sets of residues. Numbers having exactly two non-unitary prime factors. Numbers having exactly three non-unitary prime factors. Numbers having exactly four non-unitary prime factors. Numbers having exactly five non-unitary prime factors.