A Fermat number is defined as: fi = 5-1 -2fi-1 + 2 with fo = 3. (a) Set up, and solve, a recurrence relation to calculate the number of additions and sub- tractions carried out in the computation of the th Fermat number, given this recursive definition. (b) It has been shown that the growth of the Fermat numbers is doubly exponential, with the closed-form formula: 2(2") +1. Prove that the growth of the Fermat numbers is at least 12 (10")