On two classes of simultaneous Pell equations with no solutions
On two classes of simultaneous Pell equations with no solutions
In this paper we describe two classes of simultaneous Pell equations of the form <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x squared minus d y squared equals z squared minus e y squared equals 1"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>−<!-- − --></mml:mo> <mml:mi>d</mml:mi> <mml:msup> <mml:mi>y</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>z</mml:mi> …