Due at 10:15am in class, Monday, February 4, 2005

Solutions may be submitted in person in class,
or you may email an ASCII text,
html, or postscipt/pdf-formatted document to me.

Note my office hours on my
schedule.

- Prove by induction that for the Fibonacci number
f_n, f_0 = f_1 = 1, f_{n+2} = f_{n+1} + f_n for all n ≥ 2 one has

f_n = 1/sqrt(5) ( ((1 + sqrt(5))/2)^(n+1) - ((1-sqrt(5))/2)^(n+1) ).

(cf. the Binet formula in ENT, §14.3, p.196.) - ENT, §1.2, Problem 10, page 12.
- ENT, §2.2, Problem 14, page 25.
- ENT, §2.3, Problem 2(d), page 31. Please compute the Bezout coefficients by the extended Euclidean algorithm presented in class, not the back-substitution given in the book.
- Prove for the extended Euclidean algorithm described in class:
*s*for all_{k}t_{k+1}- s_{k+1}t_{k}= (-1)^{k+1}*-1 ≤ k ≤ n*