fix: integer overflow in MobiusFunction

[SEPURI-SAI-KRISHNA]

Problem

MobiusFunction.mobius decides whether a prime factor is repeated with number % (i * i) == 0, where i is an int. The product overflows for i > 46340, and the wrapped value can still divide number, which makes the method report a squared prime factor that does not exist.

The worst case is Integer.MAX_VALUE, whose square wraps to exactly 1. Since every number is divisible by 1, the method returns 0 for it:

MobiusFunction.mobius(2147483647);  // returns 0, expected -1 (2147483647 is prime)

Separately, the loop for (int i = 1; i <= number; i++) calls PrimeCheck.isPrime(i) on every value up to number, so the method is O(n * sqrt(n)). mobius(2147483647) performs on the order of 2^31 iterations, each with a primality check.

Fix

Replaced the scan over all candidates with ordinary trial division that divides each prime factor out of a running remainder:

• the loop bound is (long) factor * factor <= remaining, widened to long so it cannot overflow near Integer.MAX_VALUE;
• a factor found twice in a row means a squared prime factor, so the method returns 0;
• whatever remains after the loop is either 1 or a single prime larger than the square root, and is counted once.

This removes the overflow and drops the complexity from O(n * sqrt(n)) to O(sqrt(n)) — mobius(Integer.MAX_VALUE) now returns immediately. The explicit number == 1 early return is no longer needed: the loop does not execute and the factor count of 0 yields 1, which is the same result.

Behaviour is otherwise unchanged, including the IllegalArgumentException for non-positive input.

Tests

MobiusFunctionTest previously only checked 1..100, all of which are well below the overflow threshold. Added a parameterized case over large inputs, including Integer.MAX_VALUE and its neighbours, perfect powers of two, 46340^2 and large primes. mobius(2147483647) fails on the old code.

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[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 80.58%. Comparing base (56e2699) to head (d84a5a5).

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #7574      +/-   ##
============================================
- Coverage     80.59%   80.58%   -0.01%     
+ Complexity     7483     7481       -2     
============================================
  Files           815      815              
  Lines         24060    24062       +2     
  Branches       4736     4736              
============================================
+ Hits          19390    19391       +1     
  Misses         3907     3907              
- Partials        763      764       +1     

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