[10 marks] The following statement is useful when arguing about the correctness of the binary algorithm of computing the greatest common divisor: Let d be a positive integer, and u and v be positive odd integers with u > '1). Then dlu and dlv if and only if (Mu 'U)/2 and dlv. Now prove this statement is true. Note that you are NOT asked to use this statement to argue about the correctness of the binary algorithm. Rather, you are asked to prove the above statement itself. Hint: Make sure to prove both the \"if\" and \"only if\" in this claim.|