QUADRATIC DIOPHANTINE EQUATIONS WITH APPLICATIONS TO QUARTIC EQUATIONS

摘要

In this paper, we first show that, under certain conditions, the solution of a single quadratic diophantine equation in four variables Q(x(1), x(2), x(3), x(4)) = 0 can be expressed in terms of bilinear forms in four parameters. We use this result to establish a necessary, though not sufficient, condition for the solvability of the simultaneous quadratic diophantine equations