  An infinite integer matrix A is called image partition regular if, whenever
the natural numbers are finitely coloured, there is an integer vector x such
that Ax is monochromatic. Given an image partition regular matrix A, can we
also insist that each variable x_i is a multiple of some given d_i? This is a
question of Hindman, Leader and Strauss.
  Our aim in this short note is to show that the answer is negative. As an
application, we disprove a conjectured equivalence between the two main forms
of partition regularity, namely image partition regularity and kernel partition
regularity.
