By Kenneth H. Rosen
ISBN-10: 0321538013
ISBN-13: 9780321538017
Read or Download Instructor's Solutions Manual for Elementary Number Theory and Its Applications, 6th Ed. PDF
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Extra resources for Instructor's Solutions Manual for Elementary Number Theory and Its Applications, 6th Ed.
Sample text
Thus we will need to multiply 2k × 2k matrices seven times, requiring 7 · 7k = 7k+1 multiplications. Similarly, we will need to add 2k × 2k matrices 18 times, requiring exactly 18 · 2k additions. But 18 · 2k < 7 · 3 · 2 · 2k−1 < 72 · 2k−1 < 7k+1 , as desired. 23. Let k = [log2 n] + 1. Then the number of multiplications for 2k × 2k matrices is O(7k ). But, 7k = 2(log2 7)([log2 n]+1) = O(2log2 n log2 7 2log2 7 ) = O(nlog2 7 ). The other bit operations are absorbed into this term. Copyright c 2011 Pearson Education, Inc.
2 is composite. 27. For n = 0, 1, 2, . . 10, the values of the function are 11, 13, 19, 29, 43, 61, 83, 109, 139, 173, 211, each of which is prime. But 2 · 112 + 11 = 11(2 · 11 + 1) = 11 · 23, so it is not prime. 28. For n = 1, 2, . . 28, the values of the function are 31, 37, 47, 61, 79, 101, 127, 157, 191, 229, 271, 317, 367, 421, 479, 541, 607, 677, 751, 829, 911, 997, 1087, 1181, 1279, 1381, 1487, 1597, each of which is prime. But 2 · 292 + 29 = 29(2 · 29 + 1) = 29 · 59, so it is not prime.
Then we add the bits 1 and 1 and the carry 1, obtaining the fifth bit from the right in the sum 1, and the carry 1. Then we add the bits 1 and 1 and the carry obtaining the sixth bit from the right in the sum 1, and the carry 1. Then we add the bits 1 and 0 and the carry 1 obtaining the seventh bit from the right in the sum, 0, and the carry, 1. Then we add the bits 0 and 0 and the carry 1, obtaining the eighth bit from the right in the sum 1. Then we add the bits 1 and 1, obtaining the ninth bit from the right, 0, and the carry 1.
Instructor's Solutions Manual for Elementary Number Theory and Its Applications, 6th Ed. by Kenneth H. Rosen
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