Effective lower bounds of the p-adic distance between powers of algebraic numbers

We use the new tool of interpolation determinants to get precise lower bounds for the p-adic distance between two integral powers of algebraic numbers. This work is the p-adic analogue of the two papers (M. Laurent, Acta Arith. 66, No. 2 (1994), 181-199; M. Laurent et al., J. Number Theory 55 (1995), 255-321) on which it is based, although several new specific p-adic ideas are introduced here. (C) 1996 Academic Press, Inc.