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# Asymptotic Analysis and Fibonacci Number

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Q.1 For a number x, with 1< x < p, the number x^n mod p can be computed with at most 2log2 n modulo p multiplications.

Asymptotic notation questions
Q.2 2^(2n) = O(2^n)
Q.3 log*n = O(log*(log n))

Q.4 The sqrt n th Fibonacci number can be computed and written in O(log n) time

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https://brainmass.com/math/number-theory/asymptotic-analysis-fibonacci-number-45149

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Q.1

For a number x, with 1 x p, the number can be computed with at most
modulo p multiplications.

It is true. By Modular Arithmetic, we know that
mod p) (b mod p)] mod p
mod ] mod p
So, when we compute , it suffices to write n in the form of

Since any positive integer can have a binary code ...

#### Solution Summary

Asymptotic Analysis and Fibonacci Number are investigated.

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