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I want some hints in how to solve these questions:

How can I separate two different point by polynomial in the coordinate ring $\ k[X] $?

Many thanks

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What is the question in #1? – Zev Chonoles Feb 28 '11 at 8:47
This is not only poorly phrased, it is poorly typeset. And your comment below does nothing to explain what $N(a)$ is supposed to mean. You write "$N(a)=b^2+15c^2$", and then say $b$ and $c$ are integers. Any integers? Integers related to $a$ in some way? If you cannot make an effort to write a coherent question, why should anyone make an effort to help you? – Arturo Magidin Feb 28 '11 at 17:09
Please do not substantially change a question after an answer has been posted, especially not without an explicit note saying this has occurred. It can make an answer that was correct when posted suddenly look incorrect, and cause people do downvote unjustly. – Arturo Magidin Mar 5 '11 at 1:00
  1. This question needs clarification. What is $N(\ a)$?

  2. Hint: look at coordinate projections.

Edit: Concerning 1: If $b$ and $c$ are integers, then $b^2+15c^2$ is non-negative, so it can never be -2 or -5. If $c>0$ then $b^2+15c^2\geq 15$. If $c=0$ then $b^2+15c^2=b^2$ is a square number and thus cannot be 2 or 5 either.

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@saba: What are $b$, $c$? – Rasmus Feb 28 '11 at 10:20
@saba: This is nonsense as written. How are $b$ and $c$ related to $a$? – Arturo Magidin Feb 28 '11 at 17:07

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