Y by Adventure10
Let
be an odd prime number, and let
denote the field of integers modulo
. Let
be the ring of polynomials over
, and let
be given by
where
mod
. Find the greatest nonnegative integer
such that
divides
in
.



![$\mathbb{F}_p[x]$](http://latex.artofproblemsolving.com/e/5/a/e5a21492095c9116b100e2f7626a70cc26834e82.png)

![$q(x) \in \mathbb{F}_p[x]$](http://latex.artofproblemsolving.com/2/4/e/24e574b86f85cc81ad02b34d6d4ec576a53a95ae.png)






![$\mathbb{F}_p[x]$](http://latex.artofproblemsolving.com/e/5/a/e5a21492095c9116b100e2f7626a70cc26834e82.png)
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