Published online by Cambridge University Press: 26 February 2010
This paper gives an algorithm for generating all the solutions in integers x0, x1…, xn of the inequality
where 1, α1, …,αn are numbers, linearly independent over the rationals, in a real algebraic number field of degree n + 1 ≥ 3 and c is any sufficiently large positive constant. It is well known [2, p. 79] that if c is small enough, then (1) has no integer solutions with x1…, xn not all zero.