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Nov 1, 2013 at 20:25 comment added fedja Correct.$\phantom{uuu}$
Nov 1, 2013 at 13:35 comment added GH from MO I admire your skills. So you prove that there is $N$ whose support is not in $U$, then reduction to a prime divisor of $N$ not in $U$ produces the final $N$, right? I would add this remark for clarity.
Nov 1, 2013 at 12:39 history answered fedja CC BY-SA 3.0