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I got a problem. I don't know how to solve this kind of problem:

Find an integer $n_0$ that for each $n>n_0$ this inequation would be always true:

$\dfrac{n^{4}-n^{2}+1}{n^{3}-n}>10000 $

I don't know how to solve this kind of problems, and I hope you could help me understanding how to proceed step by step. Thank you in advance.

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    Finding any integer $n_0$ where the inequality is true, that is easy. Finding the smallest integer requires only slightly more work.2011-01-26

2 Answers 2

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Hints:

$\dfrac{n^{4}-n^{2}+1}{n^{3}-n}>10000\Leftrightarrow n+\dfrac{1}{n^{3}-n}>10000 $

$0<\dfrac{1}{n^{3}-n}<1\Leftrightarrow n>1$

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    It is a possible valid approach.2011-01-26
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Can you divide out the fraction to a polynomial and remainder? That will help.