feat(Data/ZMod/Basic): unit characterization for ZMod (p ^ d)

[tautschnig]

Add two lemmas characterizing units in ZMod (p ^ d) for a prime p:

• ZMod.isUnit_natCast_of_not_dvd_pow: a natural number not divisible by p is a unit in ZMod (p ^ d).
• ZMod.prime_natCast_not_isUnit_pow: the prime p is not a unit in ZMod (p ^ d) when d ≥ 1.

These complement the existing isUnit_prime_iff_not_dvd (which characterizes when a prime is a unit in ZMod n) by characterizing when an arbitrary natural number is a unit in ZMod (p ^ d).

Motivation. Arithmetic verification over fixed-width bitvectors works in ZMod (2 ^ d). A Gröbner basis solver over this ring needs to know which constants are invertible: odd constants are units (enabling algebraic simplification), while even constants are not (requiring fallback to SAT). These lemmas formalize that characterization for any prime, not just 2.

Further work related to Gröbner basis will be published once #29203 (and, before that, #34873) have been merged.

---

[github-actions]

Welcome new contributor!

Thank you for contributing to Mathlib! If you haven't done so already, please review our contribution guidelines, as well as the style guide and naming conventions. In particular, we kindly remind contributors that we have guidelines regarding the use of AI when making pull requests.

We use a review queue to manage reviews. If your PR does not appear there, it is probably because it is not successfully building (i.e., it doesn't have a green checkmark), has the awaiting-author tag, or another reason described in the Lifecycle of a PR. The review dashboard has a dedicated webpage which shows whether your PR is on the review queue, and (if not), why.

If you haven't already done so, please come to https://leanprover.zulipchat.com/, introduce yourself, and mention your new PR.

Thank you again for joining our community.

[github-actions]

PR summary 04e84bf966

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ isUnit_natCast_of_not_dvd_pow
+ prime_natCast_not_isUnit_pow

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.

---

No changes to technical debt.

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).