[nishithadaryn]

Description of Change

Adds an implementation of the happy number check in math/happy_number.cpp.
It repeatedly replaces a number with the sum of the squares of its digits and
uses a set to detect cycles. Includes self-tests.

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: Adds a happy number checker using digit-square sums with cycle detection.