...For my proofwriting class, I have to show that when , with . I know the eventual proof will be by induction, but I am not sure where to determine what the value of . Messing around with the numbers 1-9, I was able to generalize it to two cases: If is even, then and if is odd, then , but is there a way to generalize what must equal for ANY natural number ?

Edit: Looking at , my generalization doesn't seem to hold. Now I am definitely confused.

Edit2: And just to clarify, I want to be the least possible value.