fix(math): remove interactive console input from extended_euclid_algo…

[divyanshutata09]

Description of Change

Fixes #2990

• Removed interactive std::cin console inputs from math/extended_euclid_algorithm.cpp to prevent CI automated testing failures.
• Added self-contained unit tests using assert() covering coprime numbers, identical inputs, and prime values.
• Verified that all assertions pass locally with C++17 flags.

Checklist

• Added description of change
• Added file name matches File name guidelines
• Added tests and example, test must pass
• Added documentation so that the program is self-explanatory and educational - Doxygen guidelines
• Relevant documentation/comments is changed or added
• PR title follows semantic commit guidelines
• Search previous suggestions before making a new one, as yours may be a duplicate.
• I acknowledge that all my contributions will be made under the project's license.

Notes: Replaced interactive input with automated assert test cases for CI compatibility.

[divyanshutata09]

Hi maintainers, the PR is currently blocked because the required workflows are awaiting approval and the code-owner reviews are pending. Could someone please approve the workflows and review the PR when convenient? Thank you!