Ben Barber and Imre Leader, Journal of Combinatorics, Volume 4 (2013), Number 3 PDF
Does a partition regular system remain partition regular if we ask that each variable 
is divisible by 
? Not necessarily. This answers several open questions from Hindman, Leader and Strauss’s 2003 survey.
The proof of Proposition 5 in the journal version is not entirely clear; I recommend reading the updated pdf linked above. My thanks to Boaz Tsaban for pointing this out.