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PRACTICAL SOLUTION OF THE DIOPHANTINE EQUATION

Let p be an odd prime and a, b positive integers. In this note we prove that the problem of the determination of the integer solutions to the equation y2 = x(x + 2apb)(x − 2apb) can be easily reduced to the resolution of the unit equation u + √ 2v = 1 over Q( √ 2, √ p). The solutions of the latter equation are given by Wildanger’s algorithm.