mylcg.py

from math import gcd

A = [
    174383810491743830225526218886287207533,
    191898588380470994796266700002182515717,
    108820603600940618360722782640387198241,
    28574471588060987423539859812861556763,
    172011087897023844205124286337241769048,
    250552366381352896489045147880398294362
]

def main():
    D, m = solve_for_m(A)
    print(f"m: {m}")

    x = get_x(D, m)
    print(f"x: {x}")

    y = get_y(A, x, m)
    print(f"y: {y}")

    check_As(A, x, y, m)

    next_A = get_next_A(A, x, y, m)
    print(f"Next A is {next_A}")

def solve_for_m(A):
    D = []
    index = len(A) - 1

    while index > 0:
        D.append(A[index] - A[index-1])
        index -= 1

    D.reverse()

    R = []
    index = len(D) - 1
    while index > 1:
        R.append(abs(D[index]*D[index-2] - D[index-1]**2))
        index -= 1

    return D, gcd(*R)

def get_x(D, m):
    return (D[1] * pow(D[0], -1, m)) % m

def get_y(A, x, m):
    return (A[1] - x*A[0]) % m

def check_As(A, x, y, m):
    index = 1

    while index < len(A):
        calculated_A = (x * A[index-1] + y) % m
        match = "yes" if A[index] == calculated_A else "no"
        print(f"A[{index}]: {match}")

        index += 1

def get_next_A(A, x, y, m):
    return (x * A[-1] + y) % m

if __name__ == "__main__":
    main()