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# (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

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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].

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##### 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.

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