### Abstract

Consider the polynomial Pell's equation X^{2} - DY^{2} = 1, where D = A^{2} + 2C is a monic polynomial in Z[x] and deg C < deg A. Then for A, C ∈ script Q sign[x], deg C < 2, and B = A/C ∈ script Q sign[x], a necessary and sufficient condition for the polynomial Pell's equation to have a nontrivial solution in Z[x] is obtained.

Original language | English |
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Pages (from-to) | 993-1006 |

Number of pages | 14 |

Journal | Proceedings of the American Mathematical Society |

Volume | 131 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2003 Apr 1 |

### Keywords

- Polynomial Pell's equation

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Webb, W. A., & Yokota, H. (2003). Polynomial Pell's equation.

*Proceedings of the American Mathematical Society*,*131*(4), 993-1006. https://doi.org/10.1090/S0002-9939-02-06934-4