feat(FieldTheory/Finite): irreducible polynomial divides X^q^n - X iff degree divides n

[alainchmt]

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Add the theorem saying that, for an irreducible polynomial f over a finite field K, the degree of f divides n if and only if f divides X ^ (Nat.card K) ^ n - X. Include auxiliary lemmas.

[github-actions]

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[github-actions]

PR summary a7c945e01f

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ Irreducible.dvd_X_pow_card_pow_natDegree_sub_X
+ Irreducible.dvd_X_pow_card_pow_sub_X_of_natDegree_dvd
+ Irreducible.natDegree_dvd_iff_dvd_X_pow_card_pow_sub_X
+ _root_.Irreducible.dvd_of_aeval_eq_zero

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

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No changes to strong technical debt.

No changes to weak technical debt.