×
Log in to StudySoup
Get Full Access to Thousands of Study Materials at Your School
Join StudySoup for FREE
Get Full Access to Thousands of Study Materials at Your School

Already have an account? Login here
×
Reset your password

# (a) If Ck = Pk/qk denotes the kth convergent of the finite simple continued fraction[1;

ISBN: 9780073383149 413

## Solution for problem 6 Chapter 15

Elementary Number Theory | 7th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Elementary Number Theory | 7th Edition

4 5 1 329 Reviews
17
3
Problem 6

(a) If Ck = Pk/qk denotes the kth convergent of the finite simple continued fraction[1; 2, 3, 4, ... , n, n + 1] , show thatPn = nPn-1 + npn-2 + (n - l)Pn-3 + + 3p1 + 2po +(po+ 1)[Hint: Add the relations Po = 1, P1 = 3, Pk = (k + OPk-1 + Pk-2 for k =2, ... , n.](b) Illustrate part (a) by calculating the numerator p4 for the fraction [l; 2, 3, 4, 5].

Step-by-Step Solution:
Step 1 of 3

I D ... 00 -o.QD\'2L\ I • \0 • • n / ... •

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383149

Elementary Number Theory was written by and is associated to the ISBN: 9780073383149. The full step-by-step solution to problem: 6 from chapter: 15 was answered by , our top Math solution expert on 03/14/18, 05:19PM. Since the solution to 6 from 15 chapter was answered, more than 225 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 16 chapters, and 355 solutions. This textbook survival guide was created for the textbook: Elementary Number Theory, edition: 7. The answer to “(a) If Ck = Pk/qk denotes the kth convergent of the finite simple continued fraction[1; 2, 3, 4, ... , n, n + 1] , show thatPn = nPn-1 + npn-2 + (n - l)Pn-3 + + 3p1 + 2po +(po+ 1)[Hint: Add the relations Po = 1, P1 = 3, Pk = (k + OPk-1 + Pk-2 for k =2, ... , n.](b) Illustrate part (a) by calculating the numerator p4 for the fraction [l; 2, 3, 4, 5].” is broken down into a number of easy to follow steps, and 80 words.

#### Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

(a) If Ck = Pk/qk denotes the kth convergent of the finite simple continued fraction[1;