A Method to Solve the Diophantine Equation $ax^2-by^2+c=0$

dc.creatorSmarandache, Florentin
dc.date2006-09-24
dc.date.accessioned2026-07-07T07:25:12Z
dc.date.available2026-07-07T07:25:12Z
dc.descriptionIt is a generalization of Pell's equation $x^2-Dy^2=0$. Here, we show that: if our Diophantine equation has a particular integer solution and $ab$ is not a perfect square, then the equation has an infinite number of solutions; in this case we find a close expression for $(x_n,y_n)$, the general positive integer solution, by an original method. More, we generalize it for any Diophantine equation of second degree and with two unknowns $f(x,y)=0$.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0609671
dc.identifierhttp://arxiv.org/abs/math/0609671
dc.identifierGaceta Matematica, 2a Serie, Vol. 1, No. 2, 1988, pp. 151-157; translated into Spanish by Francisco Bellot Rosado, "Un metodo de resolucion de la ecuacion diofantica"
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116638
dc.subjectGeneral Mathematics
dc.subject11D09
dc.titleA Method to Solve the Diophantine Equation $ax^2-by^2+c=0$
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