3 [10 points (a) 5 points] Let k be a positive integer. Prove that the language: {re {a, b). I #a(z) E 0 (mod k)) can not be accepted by any deterministic finite automaton with fewer than k states. Note that, for any integers u and u, and positive integer k, we write u u (mod k) to mean that the integer-division results in a remainder of u