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Proportionally modular Diophantine inequalities. (English) Zbl 1039.20036
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.

20M14 Commutative semigroups
11D75 Diophantine inequalities
Full Text: DOI
[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
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