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Prove that 9 u,+24 . if and only if 9u, Hint: Use identity (1) om page 288.

Prove that 9 u,+24 . if and only if 9u, Hint: Use identity (1) om page 288.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 9 please 

because u7 = 13 > 10. Now assume that the inequality holds for on Uk in terms of previous = U5n+7 can be used several times to express u 5(n+1)+2 numbers to arrive at Fibonacs 1 U 5n+7 = 8u5n+2+ 5u5n+1 > 8u5n+2 +2(U5n+1 +U5n) completing the induction step and the argument. It may not have escaped attention that in the portion of the Fibonacci hat we have written down, successive terms are relatively prime. This is no accident is is now proved. Theorem 14.1. For the Fibonacci sequence, gcd(un, Un+1) = 1 for every n > 1. Proof. Let us suppose that the integer d > 1 divides both un and un+1· Then thêr difference un+1 – Un = Un-1 is also divisible by d. From this and from the relant
Transcribed Image Text:because u7 = 13 > 10. Now assume that the inequality holds for on Uk in terms of previous = U5n+7 can be used several times to express u 5(n+1)+2 numbers to arrive at Fibonacs 1 U 5n+7 = 8u5n+2+ 5u5n+1 > 8u5n+2 +2(U5n+1 +U5n) completing the induction step and the argument. It may not have escaped attention that in the portion of the Fibonacci hat we have written down, successive terms are relatively prime. This is no accident is is now proved. Theorem 14.1. For the Fibonacci sequence, gcd(un, Un+1) = 1 for every n > 1. Proof. Let us suppose that the integer d > 1 divides both un and un+1· Then thêr difference un+1 – Un = Un-1 is also divisible by d. From this and from the relant
which was enerypted for a user with public key n -: 9. Prove that 9 u, +24 if and only if 9 u,. Hint: Use identity (1) on page 288. 10. Establish the following Fibonacci identity: () 28 USUS
Transcribed Image Text:which was enerypted for a user with public key n -: 9. Prove that 9 u, +24 if and only if 9 u,. Hint: Use identity (1) on page 288. 10. Establish the following Fibonacci identity: () 28 USUS
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