On the least positive solution to a proportionally modular Diophantine inequality

Alessio Moscariello

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arXiv · 1312.5126

On the least positive solution to a proportionally modular Diophantine inequality

Alessio Moscariello

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Abstract

Given three positive integers $a,b,c$, a proportionally modular Diophantine inequality is an expression of the form $ax \mod{b} \le cx$. Our aim is to give a recursive formula for the least solution to such an inequality. We then use the formula to derive an algorithm. Finally, we apply our results to a question of Rosales and Garc\'ia-S\'anchez.

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Alessio Moscariello. 2013-12-18. On the least positive solution to a proportionally modular Diophantine inequality. https://arxiv.org/abs/1312.5126

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