Solving exponential diophantine equations using lattice basis reduction algorithms

B.M.M. Weger, de

doi:10.1016/0022-314X(87)90088-6

Solving exponential diophantine equations using lattice basis reduction algorithms

B.M.M. Weger, de

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

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 <yd in x, y ¿ S for fixed d ¿ (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.

Original language	English
Pages (from-to)	325-367
Number of pages	43
Journal	Journal of Number Theory
Volume	26
Issue number	3
DOIs	https://doi.org/10.1016/0022-314X(87)90088-6
Publication status	Published - 1987

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title = "Solving exponential diophantine equations using lattice basis reduction algorithms",

abstract = "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 <yd in x, y ¿ S for fixed d ¿ (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.",

author = "{Weger, de}, B.M.M.",

year = "1987",

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publisher = "Academic Press Inc.",

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PY - 1987

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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 <yd in x, y ¿ S for fixed d ¿ (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 <yd in x, y ¿ S for fixed d ¿ (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

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