A Method of Solving a Dophantine Equation of Second Degree with N Variables

dc.creatorSmarandache, Florentin
dc.date2004-05-12
dc.date.accessioned2026-07-07T05:08:09Z
dc.date.available2026-07-07T05:08:09Z
dc.descriptionFirst, we consider the equation $ax^2 - by^2 + c = 0$, with $a,b \in N*$ and $c \in Z*$, which is a generalization of Pell's equation. Here, we show that: if this equation has an integer solution and $ab$ is not a perfect square, then it has infinitely many integer solutions; in this case we find a closed expression for $(x_{n}, y_{n})$, the general positive integer solution, by an original method. More, we generalize it for a Diophantine equation of second degree and with n variables of the form: $\sum_{i=1}^{n} a_{i}x_{i}^{2} = b$.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0405206
dc.identifierhttp://arxiv.org/abs/math/0405206
dc.identifier"Gaceta Matematica," Madrid, 2a Serie, Volumen 1, Numero 2, 1988, 151-157; translated to Spanish by Francisco Bellot Rosado as <Un metodo de resolucion de la ecuacion diofantica $ax^2 - by^2 + c = 0$>
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71146
dc.subjectGeneral Mathematics
dc.subject11D09
dc.titleA Method of Solving a Dophantine Equation of Second Degree with N Variables
dc.typetext

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