sol1.py

"""
Project Euler Problem 129: https://projecteuler.net/problem=129

A number consisting entirely of ones is called a repunit. We shall define R(k) to be
a repunit of length k; for example, R(6) = 111111.

Given that n is a positive integer and GCD(n, 10) = 1, it can be shown that there
always exists a value, k, for which R(k) is divisible by n, and let A(n) be the least
such value of k; for example, A(7) = 6 and A(41) = 5.

The least value of n for which A(n) first exceeds ten is 17.

Find the least value of n for which A(n) first exceeds one-million.
"""


defleast_divisible_repunit(divisor: int) ->int:
"""
 Return the least value k such that the Repunit of length k is divisible by divisor.
 >>> least_divisible_repunit(7)
 6
 >>> least_divisible_repunit(41)
 5
 >>> least_divisible_repunit(1234567)
 34020
 """
ifdivisor%5==0ordivisor%2==0:
return0
repunit=1
repunit_index=1
whilerepunit:
repunit= (10*repunit+1) %divisor
repunit_index+=1
returnrepunit_index


defsolution(limit: int=1000000) ->int:
"""
 Return the least value of n for which least_divisible_repunit(n)
 first exceeds limit.
 >>> solution(10)
 17
 >>> solution(100)
 109
 >>> solution(1000)
 1017
 """
divisor=limit-1
ifdivisor%2==0:
divisor+=1
whileleast_divisible_repunit(divisor) <=limit:
divisor+=2
returndivisor


if__name__=="__main__":
print(f"{solution() =}")