Ah, you are right. I had missed that F0 = 1.

With that, 2 is indeed correct.

Regarding (1), I am pretty sure it isn't the same either way.

m_k >= a_k, hence a_k mod m_k is either 0 or a_k , so with a set of triplets that is limited in size, a_k mod m_k couldn't be any natural number.