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The Diophantine equation <i>a</i><i>x</i><sup>2</sup> + 2<i>b</i><i>x</i><i>y</i> − 4<i>a</i><i>y</i><sup>2</sup> = ±1
We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation a x 2 + 2 b x y − 4 a y 2 = ±1, where a and b are nonnegative integers. The discussion is relative to the solution …