• A METHOD TO SOLVE THE DIOPHANTINE EQUATION x^2-12y^2+3=0
Abstract
Diophantine equation are fascinating to analyze and realize the study of Diophantine equation and to find their solutions would continue to puzzle both mathematicians and amateurs alike . we consider the equation
(1) with and
It is a particular case of Pell‘s equation: . Here, we show that: if the equation has an integer solution and 1.12=12 is not a perfect square, then (1) has infinitude of integer solution, in this case we find a closed expression for ,the general positive integer solution ,by an original method. more, we generalize it for any Diophantine equation of second degree and with two unknowns.
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