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a) Let m, n, r ∈ N∗ be positive integers, such that r is the remainder of the division of the number m by the number n. Show that the remainder of the dividion of the number M = 2^m −1 by N = 2^n −1 is R = 2^r − 1. b) Show that for any positive integers m, n the following equality holds: (2^m −1,2^n −1)=2^(m,n) −1.