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7,Prove the following fact: for any two positive integer a and b, gcd(2ª – 1, 2° – 1) = 29cd(a,b)–1. (hint 1: You have the following factorzation 2nm – 1 = (2" –- 1)(2"(m-1) + 2n(m-2) + 2n(m-3) hint 2: Assume a > b, 2ª – 1 = (2ª – 2ª-b) + (2ª-b – 2ª– 2b) + with a = nb + r.) + 1), +..... + (2ª-(n-1)b – 2")+ (2" – 1) .....

7,Prove the following fact: for any two positive integer a and b, gcd(2ª – 1, 2° – 1) = 29cd(a,b)–1. (hint 1: You have the following factorzation 2nm – 1 = (2" –- 1)(2"(m-1) + 2n(m-2) + 2n(m-3) hint 2: Assume a > b, 2ª – 1 = (2ª – 2ª-b) + (2ª-b – 2ª– 2b) + with a = nb + r.) + 1), +..... + (2ª-(n-1)b – 2")+ (2" – 1) .....

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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Discrete Mathematics for CS

7,Prove the following fact: for any two positive integer a and b, gcd(2ª – 1, 2° – 1) = 29cd(a,b)–1. (hint 1: You have the following factorzation 2nm – 1 = (2" – 1)(2"(m-1) + 2"(m-2) + 2n(m-3) hint 2: Assume a > b, 2ª – 1 = (2° – 2ª-b) + (2ª-b – 2–26) + with a = nb +r.) - т-. + 1), ..... + (2ª-(n-1)6 – 2") + (2" – 1) .....
Transcribed Image Text:7,Prove the following fact: for any two positive integer a and b, gcd(2ª – 1, 2° – 1) = 29cd(a,b)–1. (hint 1: You have the following factorzation 2nm – 1 = (2" – 1)(2"(m-1) + 2"(m-2) + 2n(m-3) hint 2: Assume a > b, 2ª – 1 = (2° – 2ª-b) + (2ª-b – 2–26) + with a = nb +r.) - т-. + 1), ..... + (2ª-(n-1)6 – 2") + (2" – 1) .....
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