Given three positive integers $a,b,c$, a proportionally modular Diophantineinequality is an expression of the form $ax \mod{b} \le cx$. Our aim is to givea recursive formula for the least solution to such an inequality. We then usethe formula to derive an algorithm. Finally, we apply our results to a questionof Rosales and Garc\'ia-S\'anchez.
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机译:给定三个正整数$ a,b,c $,比例模Diophantineinequality是形式$ ax \ mod {b} \ le cx $的表达式。我们的目标是为这种不平等问题的最小解决方案提供一个递归公式。然后,我们使用公式导出算法。最后,我们将结果应用到Rosales和Garc'ia-S \'anchez的问题中。
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