[Merged by Bors] - feat(NumberTheory/SumTwoSquares): it is decidable whether a number is the sum of two squares

[SnirBroshi]

Add a Decidable instance for the already proven theorem of being the sum of two squares.

Try #eval Finset.range 50 |>.filter (∃ x y, · = x ^ 2 + y ^ 2)

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[github-actions]

PR summary a2df56f501

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

+ Nat.mod_four_ne_three_of_mem_primeFactors_of_isSquare_neg_one
+ ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_three
+ instance {n : ℕ} : Decidable (∃ x y, n = x ^ 2 + y ^ 2)

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.

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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).

[riccardobrasca]

Thanks!

bors d+

[mathlib-bors]

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

[riccardobrasca]

Sorry, Can you also add a deprecation (maybe with a warning that the statement slightly changed)?

[SnirBroshi]

Sorry, Can you also add a deprecation (maybe with a warning that the statement slightly changed)?

Added back the original statements of the theorems I changed, with deprecations. Is this okay? (I didn't do it for the main theorem because it feels wrong to find a new name for it)

[riccardobrasca]

Sorry, Can you also add a deprecation (maybe with a warning that the statement slightly changed)?

Added back the original statements of the theorems I changed, with deprecations. Is this okay? (I didn't do it for the main theorem because it feels wrong to find a new name for it)

I mean to use an alias, explaining that the statement slightly changed, something like

@[deprecated "Note that the statement now uses ...." (since := "2025-10-15")]
alias Nat.Prime.mod_four_ne_three_of_dvd_isSquare_neg_one := Nat.mod_four_ne_three_of_mem_primeFactors_of_isSquare_neg_one

And similarly for the other declarations.

[riccardobrasca]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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