As with the previous question, we will want to subtract something from \(n\) in the inductive step. There we subtracted the largest power of 2 less than \(n\text{.}\) So what should you subtract here?

Note, you will still need to take care here that the sum you get from the inductive hypothesis, together with the number you subtracted will be a sum of distinct Fibonacci numbers. In fact, you could prove that the Fibonacci numbers in the sum are non-consecutive!