Proved by grobber ([Alexandru Chirvasitu][1]) 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).

  [1]: http://mathoverflow.net/users/9151/alexandru-chirvasitu