Question: a. The original problem posed by Fibonacci concerned pairs of rabbits. Two rabbits do not breed until they are 2 months old. After that, each pair of rabbits produces a new pair each month. No rabbits ever die. Let R(n) denote the number of rabbit pairs at the end of n months if you start with a single rabbit pair. Show that R(n) is the Fibonacci sequence.
b. Write 27 and 62 as the sum of distinct nonconsecutive Fibonacci numbers