Proved by grobber (Alexandru ChirvasituAlexandru Chirvasitu) on AoPS: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=61&t=157732
EDIT: Also, http://www.artofproblemsolving.com/Forum/viewtopic.php?f=38&t=335001 might contain a solution (posts #4, #7 and #8).