THE SMALLEST POSITIVE INTEGER THAT IS SOLUTION OF A PROPORTIONALLY MODULAR DIOPHANTENfE INEQUALITY

摘要

A proportionally modular Diophantine inequality is an expression of the form ax mod b ex, where a, b and c are positive integers In this paper we present an algorithm that allows us to calculate the smallest positive integer that is solution of an inequality of this type We also obtain an algorithm that computes the Frobenius number and the number of gaps of ^numerical semigroup generated by three positive integers.