### Abstract

The nonmonic polynomial Pell's equation is X ^{2} - DY ^{2} = 1, where X, Y and D = A ^{2} + 2C must be polynomials over Z. Let π be the smallest product of distinct odd primes satisfying πB = πA/C ∈ Z[x]. Then necessary and sufficient conditions for which the polynomial Pell's equation has nontrivial solutions in Z[x] are obtained.

Original language | English |
---|---|

Pages (from-to) | 89-104 |

Number of pages | 16 |

Journal | JP Journal of Algebra, Number Theory and Applications |

Volume | 24 |

Issue number | 1 |

Publication status | Published - 2012 Feb |

### Keywords

- Polynomial Pell's equations

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*JP Journal of Algebra, Number Theory and Applications*,

*24*(1), 89-104.

**Nonmonic polynomial Pell's equations.** / Yokota, H.

Research output: Contribution to journal › Article

*JP Journal of Algebra, Number Theory and Applications*, vol. 24, no. 1, pp. 89-104.

}

TY - JOUR

T1 - Nonmonic polynomial Pell's equations

AU - Yokota, H.

PY - 2012/2

Y1 - 2012/2

N2 - The nonmonic polynomial Pell's equation is X 2 - DY 2 = 1, where X, Y and D = A 2 + 2C must be polynomials over Z. Let π be the smallest product of distinct odd primes satisfying πB = πA/C ∈ Z[x]. Then necessary and sufficient conditions for which the polynomial Pell's equation has nontrivial solutions in Z[x] are obtained.

AB - The nonmonic polynomial Pell's equation is X 2 - DY 2 = 1, where X, Y and D = A 2 + 2C must be polynomials over Z. Let π be the smallest product of distinct odd primes satisfying πB = πA/C ∈ Z[x]. Then necessary and sufficient conditions for which the polynomial Pell's equation has nontrivial solutions in Z[x] are obtained.

KW - Polynomial Pell's equations

UR - http://www.scopus.com/inward/record.url?scp=84858955628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858955628&partnerID=8YFLogxK

M3 - Article

VL - 24

SP - 89

EP - 104

JO - JP Journal of Algebra, Number Theory and Applications

JF - JP Journal of Algebra, Number Theory and Applications

SN - 0972-5555

IS - 1

ER -