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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 4: Q59E (page 257)

Show that Algorithm 4 uses $O(q\log a)$bit operations, assuming thata> d .

Short Answer

Expert verified

$O(q\log a)$

Step by step solution

Step

The only time-consuming part of the algorithm is the while loop, which is iterated $q$ times. The work done inside is a subtraction of integers no bigger than$a$, which has $\log a$ bits. The results now follow from Example 9.

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Most popular questions from this chapter

Find the prime factorization of each of these integers.

a.)39 b) 81 c) 101 d) 143 e) 289 f) 899

Find $\gcd (92928, 123552)$ and $Icm (92928, 123552)$ and verify that $\gcd (92928, 123552) \cdot Icm (92928, 123552) = 92928 \cdot 123552$ . [Hint: First, find the prime factorizations of 92928 and 123552.]

Show that if $a^{m} + 1$ is composite if $a$ and $m$ are integers greater than 1 and $m$ is odd. [ Hint: Show that $x + 1$ is a factor of the polynomial $x^{m} + 1$ if $m$ is odd.]

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Show that Algorithm 4 uses \(O(q\log a)\)bit operations, assuming thata> d .

Short Answer

Step by step solution

Step

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Most popular questions from this chapter

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