### 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 |

Externally published | Yes |

### Keywords

- Polynomial Pell's equation

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

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

**Polynomial Pell's equation-II.** / Webb, W. A.; Yokota, H.

Research output: Contribution to journal › Article

*Journal of Number Theory*, vol. 106, no. 1, pp. 128-141. https://doi.org/10.1016/j.jnt.2003.12.005

}

TY - JOUR

T1 - Polynomial Pell's equation-II

AU - Webb, W. A.

AU - Yokota, H.

PY - 2004/5

Y1 - 2004/5

N2 - The polynomial Pell's equation is X2 - DY2 = 1, where D is a polynomial with integer coefficients and the solutions X, Y must be polynomials with integer coefficients. Let D = A2 + 2C be a polynomial in L[x], where deg C

AB - The polynomial Pell's equation is X2 - DY2 = 1, where D is a polynomial with integer coefficients and the solutions X, Y must be polynomials with integer coefficients. Let D = A2 + 2C be a polynomial in L[x], where deg C

KW - Polynomial Pell's equation

UR - http://www.scopus.com/inward/record.url?scp=2342532497&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2342532497&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2003.12.005

DO - 10.1016/j.jnt.2003.12.005

M3 - Article

VL - 106

SP - 128

EP - 141

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -