Describe your change:

While reading through maths/fermat_little_theorem.py I noticed a small bug in the binary_exponentiation function.

It halves the exponent with / (true division), which turns the exponent into a float. It happens to give the right answer for small inputs, but floats can't represent integers exactly beyond 2**53, so for large exponents it silently returns wrong results. The float type hint on n was a side effect of this -- an exponent here is always a whole number.

The fix is two characters: n: float -> n: int, and n / 2 -> n // 2 (floor division), so everything stays an integer and stays correct for large values.

I also added three doctests. They return 4, 1, and 8 -- the same as before -- so it's easy to confirm the fix doesn't change behavior for normal inputs.

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword.