### Abstract

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

Pages (from-to) | 325-367 |

Journal | Journal of Number Theory |

Volume | 26 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1987 |

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*Journal of Number Theory*,

*26*(3), 325-367. https://doi.org/10.1016/0022-314X(87)90088-6

}

*Journal of Number Theory*, vol. 26, no. 3, pp. 325-367. https://doi.org/10.1016/0022-314X(87)90088-6

**Solving exponential diophantine equations using lattice basis reduction algorithms.** / de Weger, B.M.M.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - Solving exponential diophantine equations using lattice basis reduction algorithms

AU - de Weger, B.M.M.

PY - 1987

Y1 - 1987

N2 - Let S be the set of all positive integers with prime divisors from a fixed finite set of primes. Algorithms are given for solving the diophantine inequality 0< x − y < yδ in x, y S for fixed δ (0, 1), and for the diophantine equation x + Y = z in x, y, z S. The method is based on multi-dimensional diophantine approximation, in the real and p-adic case, respectively. The main computational tool is the L3-Basis Reduction Algorithm. Elaborate examples are presented.

AB - Let S be the set of all positive integers with prime divisors from a fixed finite set of primes. Algorithms are given for solving the diophantine inequality 0< x − y < yδ in x, y S for fixed δ (0, 1), and for the diophantine equation x + Y = z in x, y, z S. The method is based on multi-dimensional diophantine approximation, in the real and p-adic case, respectively. The main computational tool is the L3-Basis Reduction Algorithm. Elaborate examples are presented.

U2 - 10.1016/0022-314X(87)90088-6

DO - 10.1016/0022-314X(87)90088-6

M3 - Article

VL - 26

SP - 325

EP - 367

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 3

ER -