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Apr 21, 2013 at 13:45 vote accept Liss
Apr 9, 2013 at 13:46 comment added user9072 @Liss: in case you should also need information what is and is not possible in more general situations the following paper and references there could be useful arxiv.org/abs/math/9511209
Apr 9, 2013 at 13:41 comment added Liss Yes, $p$ was intended to be prime, I included it now in the question. Thanks for the answer, and considering two sums from the left and right was the thing that I needed, as well as obtaining that only a linear combination produced from the fact that the sum of the roots is zero is a possible equality. And its great that it turns out the answer is $no$, if the number of entries $|I|+|J|< p...$
Apr 9, 2013 at 13:04 history answered Douglas Zare CC BY-SA 3.0