Show that the Fibonacci numbers satisfy the recurrence relation f_n = 5f_n - 4 + 3f_n - 5 for n = 5, 6, 7, ..., together with the initial condition f_o = 0, f_1 = 1, f_2 = 1, f_3 = 2 and f_4 = 3. (b) Use this recurrence relation to show that f_5n is divisible by 5, for n = 1, 2, 3, ... (prove by induction on n)