×
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

# Let x be an irrational number with convergents Pnf qn. For every n :'.::: 0, verify the

ISBN: 9780073383149 413

## Solution for problem 13 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 1 325 Reviews
24
5
Problem 13

Let x be an irrational number with convergents Pnf qn. For every n :'.::: 0, verify the following:1 I Pn I 1(a) < x - - < .2qnqn+l qn qnqn+l(b) The convergents are successively closer to x in the sense that[Hint: Rewrite the relationI Pn I I Pn-1 x-- < x---Iqn qn-1Xn+lPn + Pn-1x= ------Xn+lqn + qn-1as Xn+1(xqn - Pn) = -qn-1(x - Pn-ifqn-1).]

Step-by-Step Solution:
Step 1 of 3

- -1- _ Jgk _ A hjje(.,oC_m'-tc

Step 2 of 3

Step 3 of 3

#### Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Let x be an irrational number with convergents Pnf qn. For every n :'.::: 0, verify the