Use Exercise 36 to show that if a and b are posi­tive

Chapter 4, Problem 37E

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Problem 37E

Use Exercise 36 to show that if a and b are posi­tive integers, then gcd(2a- 1, 2b - 1) = 2gcd(a,b)-1. [Hint: Show that the remainders obtained when the Eu­clidean algorithm is used to compute gcd(2a -1, 2b-1) are of the form 2r - 1. where r is a remainder arising when the Euclidean algorithm is used to find gcd(a, b).]

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