2004/05/12 by Florentin Smarandache
Mathematics · #math.GM #msc:11D09
published as "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 $ax^2 - by^2 + c = 0$> · 11 pages
arxiv created 2004/05/12 · arxiv updated 2009/12/01
First, we consider the equation ax2 - by2 + c = 0, with a,b ∈ N* and c ∈ 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 (xn, yn), 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: ∑i=1n aixi2 = b.