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

VL - 26

SP - 325

EP - 367

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 3

ER -