Equivalent proportionally modular Diophantine inequalities

. We study Diophantine inequalities of the form ax mod b ≤ cx . In particular, we prove that there exists a positive integer such that for every integer n ≥ N there exist a′ , c′ (positive integers dependent of n ) such that a′ x mod n ≤ c′ x has the same solutions as the above inequality....

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Veröffentlicht in:	Archiv der Mathematik 2008, Vol.90 (1), p.24-30
Hauptverfasser:	Robles-Pérez, Aureliano M., Rosales, José Carlos
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	. We study Diophantine inequalities of the form ax mod b ≤ cx . In particular, we prove that there exists a positive integer such that for every integer n ≥ N there exist a′ , c′ (positive integers dependent of n ) such that a′ x mod n ≤ c′ x has the same solutions as the above inequality.
ISSN:	0003-889X 1420-8938
DOI:	10.1007/s00013-007-2379-9