Solving exponential diophantine equations using lattice Basis Reduction Algorithms

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Weger, B.M.M. de (1987) Solving exponential diophantine equations using lattice Basis Reduction Algorithms. Journal of Number Theory, 26 (3). pp. 325-367. ISSN 0022-314X

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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 < 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.
Item Type:Article
Copyright:© 1987 Elsevier
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Link to this item:http://purl.utwente.nl/publications/70434
Official URL:http://dx.doi.org/10.1016/0022-314X(87)90088-6
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