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Question: 1 a let n gt m be positive integers and...

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1. a) Let n > m be positive integers, and suppose that n=qm+r,0 ≤ r < m, as in the Division Algorithm.

Show that when dividing 2^n − 1 by 2^m − 1, the remainder is 2^r − 1.

b) Let n > m be positive integers, and suppose that n=qm+r, 0 ≤ r <m, as in the Division Algorithm.
Show that if q is even, then when dividing 2^n + 1 by 2^m + 1, the remainder is 2^r + 1.

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