### Abstract

The polynomial Pell's equation is X^{2} - DY^{2} = 1, where D is a polynomial with integer coefficients and the solutions X, Y must be polynomials with integer coefficients. Let D = A^{2} + 2C be a polynomial in L[x], where deg C<deg A. Then for pB = pA/C ∈ L[x], p a prime, a necessary and sufficient condition for which the polynomial Pell's equation has a nontrivial solution is obtained. Furthermore, all solutions to the polynomial Pell's equation satisfying the above condition are determined.

Original language | English |
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Pages (from-to) | 128-141 |

Number of pages | 14 |

Journal | Journal of Number Theory |

Volume | 106 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 May |

### Keywords

- Polynomial Pell's equation

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Webb, W. A., & Yokota, H. (2004). Polynomial Pell's equation-II.

*Journal of Number Theory*,*106*(1), 128-141. https://doi.org/10.1016/j.jnt.2003.12.005