### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

- Polynomial Pell's equation

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*131*(4), 993-1006. https://doi.org/10.1090/S0002-9939-02-06934-4

**Polynomial Pell's equation.** / Webb, William A.; Yokota, Hisashi.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 131, no. 4, pp. 993-1006. https://doi.org/10.1090/S0002-9939-02-06934-4

}

TY - JOUR

T1 - Polynomial Pell's equation

AU - Webb, William A.

AU - Yokota, Hisashi

PY - 2003/4

Y1 - 2003/4

N2 - Consider the polynomial Pell's equation X2 - DY2 = 1, where D = A2 + 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.

AB - Consider the polynomial Pell's equation X2 - DY2 = 1, where D = A2 + 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.

KW - Polynomial Pell's equation

UR - http://www.scopus.com/inward/record.url?scp=0037385526&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037385526&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-02-06934-4

DO - 10.1090/S0002-9939-02-06934-4

M3 - Article

AN - SCOPUS:0037385526

VL - 131

SP - 993

EP - 1006

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -