feat(blockchain): add all_diophantine_solutions with type hints & doctests

[Zhanbingli]

What does this PR do?

Adds all_diophantine_solutions(a: int, b: int, c: int, n: int = 2) -> list[tuple[int, int]]
to blockchain/diophantine_equation.py. It returns up to n integer solutions to
the linear Diophantine equation a*x + b*y = c, using extended_gcd.

Why is this needed?

• Follows project guidelines (return values, no prints).
• Improves usability: callers can programmatically get multiple solutions.
• Includes type hints, clear docstring, doctests, and proper errors.

How has this been tested?

• Doctests included in the function’s docstring.
• Ran locally:
  • python3 -m doctest -v blockchain/diophantine_equation.py ✅
  • pre-commit run --all-files ✅
  • ruff check ✅

Implementation details

• If g = gcd(a, b) does not divide c, raises ValueError.
• Computes one particular solution from extended_gcd, then enumerates general
  solutions: x = x0 + t*(b/g), y = y0 - t*(a/g) for t = 0..n-1.
• Time complexity: O(log(max(|a|,|b|))) for base solution + O(n) enumeration.
• Space complexity: O(1) besides the returned list.

Breaking changes?

None.

Dependencies added/removed?

None.

Related issues / references

N/A (can add Closes #<id> if there’s a related issue).

Checklist

• I read the project’s CONTRIBUTING guidelines.
• My code follows the style rules (pre-commit / ruff).
• I added/kept type hints for public functions.
• I added doctests (and/or unit tests) covering normal & edge cases.
• I documented time/space complexity in the docstring.
• File is in the correct directory and imports remain intact.

[Zhanbingli]

I love the blockchain