feat: 2025 imo problem3

[yuanyi-350]

• [x] depends on: #28788
• [x] depends on: #28790
• [x] depends on: #28829

---

[github-actions[bot]]

PR summary 416c1d55c0

Import changes exceeding 2%

%	File
+10.14%	Mathlib.NumberTheory.Multiplicity

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.NumberTheory.Multiplicity	700	771	+71 (+10.14%)

Import changes for all files

Files	Import difference
Mathlib.NumberTheory.Multiplicity	71

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Declarations diff

+ IsBonza + apply_dvd_pow + apply_le + apply_prime_eq_one_or_dvd_self_sub_apply + apply_prime_gt_two_eq_one + coe_nat_two_pow_pred + dvd_pow_sub + fExample + isBonza + natCast_pow_pred + not_id_apply_prime_of_gt_eq_one + not_id_two_pow + padicValNat_add_le_self + pow_two_sub_one + pow_two_sub_one_ge + result - Int.coe_nat_two_pow_pred - Int.natCast_pow_pred

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/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).

[leanprover-community-bot-assistant]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[jsm28]

Please use the format in the pull request template (.github/PULL_REQUEST_TEMPLATE.md) to indicate PR dependencies, and provide a meaningful commit message above the ---.

[yuanyi-350]

Please use the format in the pull request template (.github/PULL_REQUEST_TEMPLATE.md) to indicate PR dependencies, and provide a meaningful commit message above the ---.

I have revised it according to your suggestion.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#28788~~
• ~~leanprover-community/mathlib4#28790~~
• ~~leanprover-community/mathlib4#28829~~ By Dependent Issues (🤖). Happy coding!

[yuanyi-350]

@jcommelin , I have made all the changes as you suggested.

[yuanyi-350]

@jsm28 , I have made all the changes as you suggested.

[jcommelin]

bors d=jsm28

[mathlib-bors[bot]]

:v: jsm28 can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[jsm28]

bors r+

padicValNat_add_le_self is actually true even with p isn't prime, but padicValNat probably isn't particularly useful in the non-prime case.

[mathlib-bors[bot]]

Pull request successfully merged into master.

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