Practical solution of the diophantine equation y(2) = x(x+2(a)p(b))(x-2(a)p(b))

摘要

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 y(2) = x(x + 2(a)p(b))(x - 2(a)p(b)) can be easily reduced to the resolution of the unit equation u + root 2 upsilon = 1 over Q(root 2, root p). The solutions of the latter equation are given by Wildanger's algorithm.