Rosales, J. C.; García-Sánchez, P. A.; García-García, J. I.; Urbano-Blanco, J. M. Proportionally modular Diophantine inequalities. (English) Zbl 1039.20036 J. Number Theory 103, No. 2, 281-294 (2003). The authors study the sets of nonnegative solutions of Diophantine inequalities of the form \(ax\) mod \(b \leq cx\) with \(a, b\) and \(c\) positive integers. These sets are numerical semigroups, which are investigated and characterized. Reviewer: Robert F. Tichy (Graz) Cited in 3 ReviewsCited in 29 Documents MSC: 20M14 Commutative semigroups 11D75 Diophantine inequalities Keywords:numerical semigroups; Diophantine inequalities; Frobenius numbers PDF BibTeX XML Cite \textit{J. C. Rosales} et al., J. Number Theory 103, No. 2, 281--294 (2003; Zbl 1039.20036) Full Text: DOI References: [1] Garcı́a-Sánchez, P.A.; Rosales, J.C., Numerical semigroups generated by intervals, Pacific J. math., 191, 1, 75-83, (1999) · Zbl 1009.20069 [2] Rosales, J.C.; Branco, M.B., Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups, J. pure appl. algebra, 171, 303-314, (2002) · Zbl 1006.20043 [3] Rosales, J.C.; Branco, M.B., Decomposition of a numerical semigroup as an intersection of irreducible numerical semigroups, B. belg. math. soc-sim., 9, 372-381, (2002) · Zbl 1051.20027 [4] Rosales, J.C.; Branco, M.B., Irreducible numerical semigroups, Pacific J. math., 209, 131-143, (2003) · Zbl 1057.20042 [5] J.C. Rosales, P.A. Garcı́a-Sanchez, J.M. Urbano-Blanco, Modular Diophantine inequalities and numerical semigroups, Pacific J. Math., to appear. · Zbl 1184.20052 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.