BUUCTF Alice与Bob 1

from random import randint
from math import gcd
def PollardRho(n, f):
    x, y = randint(1, n-1), 1
    while True:
        x = f(x, n)
        y = f(f(y, n), n)
        d = gcd(abs(x-y), n)
        if d != 1:
            return d
        elif x == y:
            return n
def factorize(n):
    if n == 1:
        return []
    elif is_prime(n):
        return [n]
    else:
        f = PollardRho(n, lambda x, n: (x**2 + 1) % n)
        return factorize(f) + factorize(n // f)
def is_prime(n):
    if n <= 1:
        return False
    elif n <= 3:
        return True
    elif n % 2 == 0 or n % 3 == 0:
        return False
    i = 5
    while i**2 <= n:
        if n % i == 0 or n % (i+2) == 0:
            return False
        i += 6
    return True
n = 98554799767
print(factorize(n))

[101999, 966233]
10999966233

d450209323a847c8d01c6be47c81811a