### 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 |
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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 1 |

### Keywords

- Polynomial Pell's equations

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Yokota, H. (2012). Nonmonic polynomial Pell's equations.

*JP Journal of Algebra, Number Theory and Applications*,*24*(1), 89-104.