Equivalent proportionally modular Diophantine inequalities. (Q2475570)

The authors study Diophantine inequalities of the form \(ax\bmod b\leq cx\) and prove that there exists a positive integer \(N\in\mathbb{N}\) such that for every integer \(n\geq N\) there exist \(a',c'\) such that \(a'x\bmod n\leq c'x\) has the same solutions as the above inequality. Furthermore, relations to different subjects such as to algebraic geometry or to \(C^*\)-algebras are outlined.