On Word Equation of the Form 
In a Free Semigroup: A Further Extension
Abstract:
Word equations of the form 
are concerned in this study. In particular, I investigate the case where x is of different length than Zi, for any i and k and ki are at least 3, for all powers of the same word for all 1 i n. It is also shown that this result implies a well-known result by Appel and Djorup about the more special case where ki = kj for all 1 i< j n.