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Une borne pour les générateurs des solutions entières positives d’une équation diophantienne linéaire. (A bound for the minimal positive integer solutions of a linear diophantine equation). (French) Zbl 0615.10022
The author proves that the minimal (for the component-wise order on \({\mathbb{N}}^ k\), \(k=n+m)\) positive integer solutions of the homogeneous equation \[ \sum_{1\leq i\leq n}a_ ix_ i=\sum_{1\leq j\leq m}b_ jy_ j \] with \(a_ i\in {\mathbb{N}}^*\) and \(b_ j\in {\mathbb{N}}^*\) satisfy \[ \sum_{1\leq i\leq n}x_ i\leq_{1\leq j\leq m}b_ j\quad and\quad \sum_{1\leq j\leq m}y_ j\leq_{1\leq i\leq n}a_ i\quad. \] This improves a result of G. Huet [Inf. Process. Lett. 7, 144-147 (1978; Zbl 0377.10011)].

MSC:
11D04 Linear Diophantine equations
90C10 Integer programming
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