Leonardo Pisano Fibonacci, a famous thirteenth-century mathematician, generated the sequence of integers 10,1, 1,2, 3, 5, 8, 13, 21,34. ...^ while addressing, oddly enough, a problem in volving rabbit reproduction. An element of the Fibonacci sequence is the sum of the previous two. (a) Find the constant-coefficient difference equation whose zero-input response f[n] with aux- iliary conditions [-0 and 2s a Fibonacci sequence. Given f[n] is the system output, what is the system input? (b) What are the characteristic roots of this system? Is the system stable? (c) Designating 0 and 1 as the first and second Fibonacci numbers, determine the fiftieth Fi- bonacci number. Determine the thousandth Fibonacci number.