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Jun 25, 2013 at 3:02 review Late answers
Jun 26, 2013 at 7:04
Jul 13, 2012 at 12:56 comment added Emil Jeřábek The reasoning is not correct: the equation $p(x)-ir=0$ only holds for the isolated points $a_i$, not in their neighbourhoods, hence taking derivatives will not preserve the equality. Note that your argument never used the assumption that $a_i$’s are integers, but then the result does not hold, there are infinite arithmetic progressions with real $a_i$ (since the range of $p$ is all of $\mathbb R$ or a one-side unbounded interval).
Jul 13, 2012 at 12:38 history edited Emil Jeřábek CC BY-SA 3.0
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Jul 13, 2012 at 12:21 history answered Eduardo Jose CC BY-SA 3.0