def remainder(a: int, n: int) -> int:
    d = a * a
    return (pow(a - 1, n, d) + pow(a + 1, n, d)) % d


def max_remainder(a: int) -> int:
    n, r_max = 1, 2
    while True:
        r = remainder(a, n)
        if r == r_max:
            break
        if r > r_max:
            r_max = r
        n += 1
    assert(r_max > 2)
    return r_max


def euler_120():
    assert(remainder(7, 3) == 42)
    assert(max_remainder(7) == 42)
    return sum([max_remainder(n) for n in range(3, 1001)])


if __name__ == "__main__":
    solution = euler_120()
    print("e120.py: " + str(solution))
    assert(solution == 333082500)