  It was shown by V. Bergelson that any set B with positive upper
multiplicative density contains nicely intertwined arithmetic and geometric
progressions: For each positive integer k there exist integers a,b,d such that
$ {b(a+id)^j:i,j \in\nhat k}\subset B. $ In particular one cell of each finite
partition of the positive integers contains such configurations. We prove a
Hales-Jewett type extension of this partition theorem.
