Given a real number x and a positive integer k, determine the number of multiplications used to find x^(2^k) starting with x and successively squaring (to find x^2, x^4, and so on). Is this a more efficient way to find x^(2^k) than by multiplying x by itself the appropriate number of times?

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Q: time

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A:

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A:

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Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.