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Equivalent proportionally modular Diophantine inequalities
Authors:Aureliano M. Robles-Pérez  José Carlos Rosales
Affiliation:(1) Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, E-1 18071 Granada, Spain;(2) Departamento de álgebra, Facultad de Ciencias, Universidad de Granada, E-1 18071 Granada, Spain
Abstract:
We study Diophantine inequalities of the form ax mod bcx. In particular, we prove that there exists a positive integer 
$$N in {mathbb{N}}$$
such that for every integer nN there exist a′, c′ (positive integers dependent of n) such that a′ x mod nc′ x has the same solutions as the above inequality. Received: 23 March 2007
Keywords:Primary 20M14, 11D75  Secondary 13H10
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