The polynomial solutions of quadratic Diophantine equation \(X^2-p(t)Y^2 + 2K(t)X+2p(t) L(t)Y = 0\) (Q2666442)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The polynomial solutions of quadratic Diophantine equation \(X^2-p(t)Y^2 + 2K(t)X+2p(t) L(t)Y = 0\) |
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The polynomial solutions of quadratic Diophantine equation \(X^2-p(t)Y^2 + 2K(t)X+2p(t) L(t)Y = 0\) (English)
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22 November 2021
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Summary: In this study, we consider the number of polynomial solutions of the Pell equation \(x^2-p(t) y^2=2\) is formulated for a nonsquare polynomial \(p(t)\) using the polynomial solutions of the Pell equation \(x^2 - p( t) y^2=1\). Moreover, a recurrence relation on the polynomial solutions of the Pell equation \(x^2-p(t)y^2=2\). Then, we consider the number of polynomial solutions of Diophantine equation \(E: X^2 - p(t)Y^2 + 2K(t)X+2p(t)L(t)Y=0\). We also obtain some formulas and recurrence relations on the polynomial solution \((X_n, Y_n)\) of \(E\).
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