Use induction to prove: for any integer n 2 1, 3|(ri,3 4n + 6). Hint: this question is case sensitive, you should ONLY use k, but not K in your answers. Base case n : ,n3 4n + 6 = , which is divisible by 3. Inductive step Assume that for any k 2 , 3| , we will prove that 3| By the inductive hypothesis, there exists an integer m such that = 3m. It follows that k3 : (k+ 1)3 4(k+1) +6 = k3+ 192+ k+ By inductive hypothesis =3( ) Since m and k are integers and integers are closed under , , and must be an integer. Hence, 3|