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 |
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Pages (from-to) | 325-367 |
Number of pages | 43 |
Journal | Journal of Number Theory |
Volume | 26 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1987 |