By the inductive hypothesis and the definition of divisibility, there exists an integer r such that 7k-2k 5r. Then 7k+1_2k + 1 = 7.7k-2-2k = (5+2) 7k-2.2k. Continue simplifying the right-hand side of the equation, apply the induction hypothesis, and express the result in terms of k and r. 7k+1_2k+ 1 = 5₁

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