Solving exponential diophantine equations using lattice basis reduction algorithms

B.M.M. de Weger

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    49 Citations (Scopus)
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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.
    Original languageEnglish
    Pages (from-to)325-367
    JournalJournal of Number Theory
    Volume26
    Issue number3
    DOIs
    Publication statusPublished - 1987

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