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01.04.2020 • 
Computers and Technology

Write two different programs to compute x^n mod m (x,n and m are integers≥0).
Note that you are not allowed to use “pow” function from library
(a). powmod1(x,n,m)
It computes x^n mod m by repeated multiplications, i.e. using iteration.

(b). powmod2(x, n, m)
It computes x^n mod m by using the following inductive definition
x^0 mod m= 1
x^n mod m=〖〖(x⋅x mod m)〗^(n/2) 〗^ mod m if n is even
x^n mod m=〖(x⋅x〗^(n-1) mod m) mod m if n is odd
Discuss which the above program is more efficient using big-O notation. If you are not sure about which one is more efficient, test your code on computer, using the following data. Present the timing result to support your conclusion.
For x=29, m = 773, use n = 100,000,000, 500,000,000 and 1,000,000,000

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