Add Mobius function implementation with comprehensive tests

[Parth07-alt]

This PR implements the Mobius function μ(n) in the mathematical algorithms section, addressing issue #36.

The Mobius function is an important multiplicative function in number theory that returns:

1 if n is a square-free positive integer with an even number of prime factors
-1 if n is a square-free positive integer with an odd number of prime factors
0 if n has a squared prime factor
Closes #36

Changes Made

✅ Added
Algorithms/math/mobius/mobius.py
with efficient O(√n) implementation
✅ Added comprehensive test suite in
Algorithm_tests/math_tests/mobius_test.py
✅ Included detailed docstrings with examples and complexity analysis
✅ Implemented proper input validation and error handling

Implementation Details

The algorithm efficiently computes the Mobius function by:

Handling the special case μ(1) = 1
Checking for prime factor 2 and detecting if it appears more than once
Iterating through odd numbers up to √n to find remaining prime factors
Returning 0 immediately if any prime factor appears more than once (not square-free)
Counting distinct prime factors and returning 1 (even count) or -1 (odd count)

Testing

All 23 test cases pass successfully, covering:

✅ Special cases (μ(1) = 1)
✅ Prime numbers (μ(2), μ(3), μ(17) = -1)
✅ Square-free numbers with 2, 3, 4, and 5 distinct prime factors
✅ Numbers with squared factors (μ(4), μ(12), μ(100) = 0)
✅ Input validation for edge cases (negative, zero, non-integer inputs)

Test Results:

Ran 23 tests in 0.002s
OK
Checklist
✅Code follows the repository's existing style and structure
✅Comprehensive tests included and passing
✅Documentation and docstrings added
✅No breaking changes
✅Branch name follows conventions (mobius)