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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