Number Theory


A Method to Solve the Diophantine Equation a X2-B Y2 + C = 0

Authors: Florentin Smarandache

We consider the equation (1) ax2 - by2 + c = 0, with a,b ε N* and c ε Z*. It is a generalization of Pell's equation: x2 -Dy2 = 1. Here, we show that: if the equation has an integer solution and a.b is not a perfect square, then (1) has an infinitude of 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 any Diophantine equation of second degree and with two unknowns.

Comments: 10 pages.

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Submission history

[v1] 13 Mar 2010

Unique-IP document downloads: 76 times

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