Consider the following program, where a and n are positive integers. Input: a, n x =...

    

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Consider the following program, where a and n are positive integers. Input: a, n x = a; m = n; y while (m > 1) { if m is even } X = X*X; m = m/2; if m is odd y x*y; X = X*X; m = Output x*y = 1; = (m-1)/2; Show by induction that the above loop has the following invariant: a = xm x y. What does the above program compute? Consider the following program, where a and n are positive integers. Input: a, n x = a; m = n; y while (m > 1) { if m is even } X = X*X; m = m/2; if m is odd y x*y; X = X*X; m = Output x*y = 1; = (m-1)/2; Show by induction that the above loop has the following invariant: a = xm x y. What does the above program compute?

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The program presented in the images appears to be an implementation of an exponentiation algorithm with the goal of computing an given the positive in... View the full answer