2008
DOI: 10.1016/j.jnt.2007.11.002
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The set of solutions of a proportionally modular Diophantine inequality

Abstract: The set of solutions of the inequality ax mod b cx is a numerical semigroup. We present in this paper a tool for finding the set of minimal generators of this set, and thus the set of solutions to such an inequality. This tool will also enable us to give characterizations of those numerical semigroups that are the set of integer solutions of inequalities of this form. Finally, we give a deeper study of the embedding dimension three case.

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Cited by 14 publications
(15 citation statements)
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“…Theorem 4.4. [RGU2] Let H be a numerical semigroup with e(H) = n. Then H is proportionally modular if and only if for some rearrangement of its generators {a 1 , a 2 , ..., a n } the following conditions hold:…”
Section: Proportionally Modular Numerical Semigroupsmentioning
confidence: 99%
“…Theorem 4.4. [RGU2] Let H be a numerical semigroup with e(H) = n. Then H is proportionally modular if and only if for some rearrangement of its generators {a 1 , a 2 , ..., a n } the following conditions hold:…”
Section: Proportionally Modular Numerical Semigroupsmentioning
confidence: 99%
“…, p} such that a 1 a 2 · · · a h a h+1 · · · a p . The following result follows from Theorem 31 and Corollary 18 of [10].…”
Section: Lemma 2 (Seementioning
confidence: 80%
“…Another result that will be used several times along this paper and that appears in [10] as Remark 24 is the following.…”
Section: Remarkmentioning
confidence: 94%
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