## Abstract

In this paper all integral solutions to the equation x^{2} = 4q^{n}-4q+1 when q is an odd prime are determined. This is done by working in a quadratic field, using the unique factorization of ideals to reduce the problem to one about certain binary linear recurrences. One of the results is that the equation has no solutions with n > 2 if q > 5.

Original language | English (US) |
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Pages (from-to) | 303-309 |

Number of pages | 7 |

Journal | Pacific Journal of Mathematics |

Volume | 139 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1989 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

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