Add doctests to carmichael_number.py

[vipinkarthic]

Describe your change:

Related to

• Improve our test coverage #9943

Added Doctests to Carmichael_number.py

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

[vipinkarthic]

@cclauss

Can you take a look at the PR and let me know if I should add more doctests or if this is fine?

[cclauss]

Git conflicts.

[vipinkarthic]

Git conflicts.

Someone has modified the current while i was modifying this, so thank you for your time, I'll ping you after I find another doctest missing file and create another PR for that. Thank You !

Please close the PR.

[tianyizheng02]

@vipinkarthic I fixed the merge conflict by adding your doctests to the existing ones.