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# Assume that the continued fraction representation for the irrational number x ISBN: 9780073383149 413

## Solution for problem 12 Chapter 15

Elementary Number Theory | 7th Edition

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Problem 12

Assume that the continued fraction representation for the irrational number x ultimatelybecomes periodic. Mimic the method used in Example 15.4 to prove thatx is of the formr + s,,/d, where r and s =j:. 0 are rational numbers and d > 0 is a nonsquare integer.

Step-by-Step Solution:
Step 1 of 3

,Catl. :=. dr=fu '&x u- ftD'.t - dt ax u{ u-'3x t v' 'tv \rsa.3 vorttqW 3y. Jv U ,3th.rMl

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383149

Since the solution to 12 from 15 chapter was answered, more than 221 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Elementary Number Theory, edition: 7. This full solution covers the following key subjects: . This expansive textbook survival guide covers 16 chapters, and 355 solutions. Elementary Number Theory was written by and is associated to the ISBN: 9780073383149. The answer to “Assume that the continued fraction representation for the irrational number x ultimatelybecomes periodic. Mimic the method used in Example 15.4 to prove thatx is of the formr + s,,/d, where r and s =j:. 0 are rational numbers and d > 0 is a nonsquare integer.” is broken down into a number of easy to follow steps, and 46 words. The full step-by-step solution to problem: 12 from chapter: 15 was answered by , our top Math solution expert on 03/14/18, 05:19PM.

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