3.19 Divide-and-conquer Fibonacci. Let f denote the 2th Fibonacci number. Starting from the equation i-+ F-2 and the base case R-.prove that for any and any m 2 1 we have (3.20) In particular, prove the following: (3.21) Then show that if and p are n-bit numbers, we can calculate Fi mod p in poly(n) time. Hint: using (3.21) naively gives a running time that is polynomial in 1, but not in n = log2. 3.19 Divide-and-conquer Fibonacci. Let f denote the 2th Fibonacci number. Starting from the equation i-+ F-2 and the base case R-.prove that for any and any m 2 1 we have (3.20) In particular, prove the following: (3.21) Then show that if and p are n-bit numbers, we can calculate Fi mod p in poly(n) time. Hint: using (3.21) naively gives a running time that is polynomial in 1, but not in n = log2