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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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    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.2011-03-05

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  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: This is nonsense as written. How are $b$ and $c$ *related* to $a$?2011-02-28