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Question 2. GCDs and relative primality. (a) Prove that gcd(2a 1, 2 b 1) = 2gcd(a,b) 1. (b) Suppose you wish to choose 10 large

Question 2. GCDs and relative primality.

(a) Prove that gcd(2a 1, 2 b 1) = 2gcd(a,b) 1.

(b) Suppose you wish to choose 10 large integers m1, . . . , m10 such that they are pairwise relatively prime. How can you use (a) to come up with such integers?

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