1. Introduction

The classical circle method of Hardy and Littlewood (see Baker [1]) ensures that the diophantine equation

a1xk1+[ctdot ]+ asxks =0 (1.1)

has a nontrivial solution in nonnegative integers x1, [ctdot ], xs, provided s[ges ]C(k) and the coefficients a1, [ctdot ], as are all integers and not all the same sign.