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arXiv · 1707.07154

L'\'equation diophantienne $ax^2-by^2=1$

Lionel Ponton
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Abstract

On propose une m\'ethode de r\'esolution effective de l'\'equation diophantienne $(E_2): ax^2-by^2=1$ o\`u $a$ et $b$ sont des entiers naturels non nuls et premiers entre eux. Cette m\'ethode s'appuie sur le d\'eveloppement en fraction continu\'ee de certains nombres irrationnels quadratiques que l'on d\'ecrit compl\`etement. On commence par utiliser ces d\'eveloppements pour r\'esoudre certaines \'equations de Pell-Fermat g\'en\'eralis\'ees avant d'appliquer \`a l'\'equation $(E_2)$ les r\'esultats obtenus.

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Lionel Ponton. 2017-07-22. L'\'equation diophantienne $ax^2-by^2=1$. https://arxiv.org/abs/1707.07154

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