[akhila-pynam]

Description of Change

Refactors math/armstrong_number.cpp to fit the repository contribution guidelines:

• Enclosed functions inside namespace math.
• Replaced floating-point std::pow with an integer binary exponentiation power function to prevent precision issues.
• Fixed number_of_digits to correctly return 1 for 0.
• Added standard Doxygen docblocks (@brief, @param, @return).
• Added comprehensive self-tests with assert() covering 0, single-digit, multi-digit, and non-Armstrong cases.

Fixes part of #2456

Checklist

• Added description of change
• 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: Modernized math/armstrong_number.cpp to adhere to contribution guidelines.