Exercise 3.3.13 (Eisenstein’s criterion proof)

Question

The last step in (3.9) was $'deg(\bar h) \leq deg(h)'$. Why
is that true? And when does equality hold?

Hassaan Naeem · Accepted Answer

extbf{Solution:}
$\bar h = hmodp$. Therefore if $p|a_{n_h}$ then $a_{n_{\bar h}}=0$ and $deg(\bar h) < deg(h)$. If $p 
mid a_{n_h}$ then $a_{n_h} = a_{n_{\bar h}}$ and $deg(\bar h)= deg(h)$.
Therefore $deg(\bar h) \leq deg(h)$. Equality holds on the preceding condition.

Exercise 3.3.13 (Eisenstein’s criterion proof)

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Exercise 3.3.13 (Eisenstein’s criterion proof)

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