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# If Ck = Pk/qk is the kth convergent of the simple continued fraction [ao; ai, ... , an]

ISBN: 9780073383149 413

## Solution for problem 10 Chapter 15

Elementary Number Theory | 7th Edition

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Elementary Number Theory | 7th Edition

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Problem 10

If Ck = Pk/qk is the kth convergent of the simple continued fraction [ao; ai, ... , an] andao > 0, show thatand--qk= [ak; ak-I, ... , a1, ai]qk-1[Hint: In the first case, notice that....!!!:__ = ak + Pk-2Pk-1 Pk-11= ak + p ] k-1Pk-2

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Math 206 Fall 2016 Project 1 Generated For: bmao12 Covers: This project covers up through and including Chapter 8 of the tutorial. What to Submit: For this project you will need to create and upload a single script m-▯le called matlab1.m (all lower case!). This ▯le should do all of the things requested in the problems below in the order speci▯ed. Grading Method: Grading for this course is via an automated grading system which checks both that your answers are correct and that you used the correct method of obtaining them. This is why it is important to assign your answers to the correct variable names and use the methods speci▯ed. Use of comments (if you know how to use them) is ▯ne - comments are ignored by the grading system. I

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##### ISBN: 9780073383149

The full step-by-step solution to problem: 10 from chapter: 15 was answered by , our top Math solution expert on 03/14/18, 05:19PM. This textbook survival guide was created for the textbook: Elementary Number Theory, edition: 7. The answer to “If Ck = Pk/qk is the kth convergent of the simple continued fraction [ao; ai, ... , an] andao > 0, show thatand--qk= [ak; ak-I, ... , a1, ai]qk-1[Hint: In the first case, notice that....!!!:__ = ak + Pk-2Pk-1 Pk-11= ak + p ] k-1Pk-2” is broken down into a number of easy to follow steps, and 45 words. Elementary Number Theory was written by and is associated to the ISBN: 9780073383149. This full solution covers the following key subjects: . This expansive textbook survival guide covers 16 chapters, and 355 solutions. Since the solution to 10 from 15 chapter was answered, more than 220 students have viewed the full step-by-step answer.

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If Ck = Pk/qk is the kth convergent of the simple continued fraction [ao; ai, ... , an]