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
SN - 0022-314X
VL - 26
SP - 325
EP - 367
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 3
ER -