Python/project_euler/problem_120/sol1.py
Maxim Smolskiy 4700297b3e
Enable ruff RUF002 rule ()
* Enable ruff RUF002 rule

* Fix

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
2024-04-22 21:51:47 +02:00

33 lines
824 B
Python

"""
Problem 120 Square remainders: https://projecteuler.net/problem=120
Description:
Let r be the remainder when (a-1)^n + (a+1)^n is divided by a^2.
For example, if a = 7 and n = 3, then r = 42: 6^3 + 8^3 = 728 ≡ 42 mod 49.
And as n varies, so too will r, but for a = 7 it turns out that r_max = 42.
For 3 ≤ a ≤ 1000, find ∑ r_max.
Solution:
On expanding the terms, we get 2 if n is even and 2an if n is odd.
For maximizing the value, 2an < a*a => n <= (a - 1)/2 (integer division)
"""
def solution(n: int = 1000) -> int:
"""
Returns ∑ r_max for 3 <= a <= n as explained above
>>> solution(10)
300
>>> solution(100)
330750
>>> solution(1000)
333082500
"""
return sum(2 * a * ((a - 1) // 2) for a in range(3, n + 1))
if __name__ == "__main__":
print(solution())