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The Polynomial Solutions of Quadratic Diophantine Equation <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow> <mi>X</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>p</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> <msup> <mrow> <mi>Y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>K</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> <mi>X</mi> <mo>+</mo> <mn>2</mn…
In this study, we consider the number of polynomial solutions of the Pell equation <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>p</mi> <mfenced open="(" close=")" separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> </math> is formulated for a …