The expression p ( x ) W [ y 1 , y 2 ] ( x ) = C for all x in [ a , b ] , where C is a constant.

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Chapter 11.6, Problem 31E

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The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

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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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Answer 2

Question

Chapter 11.6, Problem 31E

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To show:

The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

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Answer 3

Question

Chapter 11.6, Problem 31E

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To show:

The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

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Answer 4

Question

Chapter 11.6, Problem 31E

To determine

To show:

The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

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Answer 5

Chapter 11.6, Problem 31E

To determine

To show:

The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

Answer 6

Chapter 11.6, Problem 31E

To determine

To show:

The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

Answer 7

Chapter 11.6, Problem 31E

To determine

To show:

The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 3E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 7E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 9E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...

The expression p ( x ) W [ y 1 , y 2 ] ( x ) = C for all x in [ a , b ] , where C is a constant.

Solution Summary: The author explains how the expressions y_1 and

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The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

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Chapter 11 Solutions

The expression p ( x ) W [ y 1 , y 2 ] ( x ) = C for all x in [ a , b ] , where C is a constant.

Solution Summary: The author explains how the expressions y_1 and

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To show: The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.

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Chapter 11 Solutions

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The expression p(x)W[y1,y2](x)=C for all x in [a,b], where C is a constant.