Add maths/repunit.py: repunit divisibility theorem

[ltianyi992]

What does this add?

Implements the repunit divisibility theorem in maths/repunit.py.

A repunit R(n) = 111...1 (n ones). The key theorem:

A prime p ≠ 2, 5 divides R(n) if and only if n is a multiple of
ord_p(10) — the multiplicative order of 10 modulo p.

This gives an O(log p) divisibility check that never needs to construct the
(potentially millions-of-digits) repunit.

Functions added

Function	Description
multiplicative_order(base, modulus)	Smallest k ≥ 1 s.t. base^k ≡ 1 (mod modulus)
repunit_length_for_prime(prime)	Smallest n s.t. prime | R(n)
is_repunit(n)	True iff n consists solely of digit 1
repunit_divisible_by(n, prime)	O(log prime) check, no giant number needed

Example

>>> repunit_divisible_by(6, 7)
True   # 111111 / 7 = 15873 exactly
>>> repunit_divisible_by(3, 7)
False  # 111 is not divisible by 7

Type hints & doctests

All functions include full type hints and passing doctests (30 tests total).

Closes #13999

References

• https://en.wikipedia.org/wiki/Repunit
• https://en.wikipedia.org/wiki/Multiplicative_order

[algorithms-keeper]

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