The only precise statement (coming from a reliable source) of the "arithmetic Nullstellensatz" I can find is in [Gower's book][1], stating that two polynomials with integral coefficients have the same roots mod every $m$ iff they differ by a sign. I would like to know the general form of this result, and see some reference where I can read about it and some applications (perhaps). All help is appreciated.


  [1]: http://books.google.ch/books?id=ZOfUsvemJDMC&pg=PA703&dq=arithmetic%20nullstellensatz&hl=de&sa=X&ei=Q7H3U5zyGcWw0QWuo4G4Aw&ved=0CCIQ6AEwATgo#v=onepage&q=arithmetic%20nullstellensatz&f=false