Given that the sequence an is the sequence of the ones digit of 3n, find the smallest positive integer A satisfying an+A = an for all positive integer n.
Lemma: Given that a ≡ c (mod n) and b ≡ d (mod n), then ab ≡ cd (mod n)
Proof: a ≡ c (mod n) and b ≡ d (mod n) implies a-c = pn and b-d = qn...