PROBLEM SOLVING APPROACH (PRINT UPGRADE)

13th Edition

ISBN: 9780135190098

Author: BILLSTEIN

Publisher: PEARSON

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Textbook Question

Chapter 6.3B, Problem 10A

Assessment

Without actually doing the computations, choose the phrase in the parentheses that correctly describes each.

a. 4 1 3 ÷ 2 1 100 ( greater than 2, less than 2 )

b. 16 ÷ 4 3 18 ( greater than 4, less than 4 )

c. 16 ÷ 3 8 9 ( greater than 4, less than 4 )

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Chapter 6.3B, Problem 9A

Chapter 6.3B, Problem 11A

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- Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., p-1 2 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). 23 32 how come? The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. The set T is the subset of these residues exceeding So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1.

Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2 multiple of n, i.e. n mod p, 2n mod p, ..., 2 p-1 -n mod p. Let T be the subset of S consisting of those residues which exceed p/2. Find the set T, and hence compute the Legendre symbol (7|23). The first 11 multiples of 7 reduced mod 23 are 7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8. 23 The set T is the subset of these residues exceeding 2° So T = {12, 14, 17, 19, 21}. By Gauss' lemma (Apostol Theorem 9.6), (7|23) = (−1)|T| = (−1)5 = −1. how come?

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Chapter 6 Solutions

PROBLEM SOLVING APPROACH (PRINT UPGRADE)

Ch. 6.1 - Mathematical Connections Explain why 25 cents is...Ch. 6.1 - Mathematical Connections In each of two different...Ch. 6.1 - Prob. 3MC Ch. 6.1 - Prob. 4MC Ch. 6.1 - Mathematical Connections Explain why in...Ch. 6.1 - Prob. 6MC Ch. 6.1 - MATHEMATICAL CONNECTIONS Explain how you could use...Ch. 6.1 - Prob. 8MC Ch. 6.1 - How would you show 14 of the combined area of the...Ch. 6.1 - Prob. 10MC

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Assessment Without actually doing the computations, choose the phrase in the parentheses that correctly describes each. a. 4 1 3 ÷ 2 1 100 ( greater than 2, less than 2 ) b. 16 ÷ 4 3 18 ( greater than 4, less than 4 ) c. 16 ÷ 3 8 9 ( greater than 4, less than 4 )

Solution Summary: The author explains that the phrase that best approximates the expression is greater than 2.

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