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Feb 11, 2012 at 6:09 comment added Fedor Petrov For the unit circle $a_p$ equals 4 for prime $p=4k+3$. I think, a priori the problem can not be reduced to components, because different components may have many points with different denominators.
Feb 10, 2012 at 19:00 history answered Felipe Voloch CC BY-SA 3.0