Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Textbook Question
Chapter 15, Problem 20A
The following problems have square roots that are not whole numbers. They require calculator computations. Refer to Unit 17 for calculator root solutions. Compute these roots to the indicated number of decimal places.
20.
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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?
Shading a Venn diagram with 3 sets: Unions, intersections, and...
The Venn diagram shows sets A, B, C, and the universal set U.
Shade (CUA)' n B on the Venn diagram.
U
Explanation
Check
A-
B
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Chapter 15 Solutions
Mathematics For Machine Technology
Ch. 15 - Raise (4+2.3)3to the indicated power.Ch. 15 - Compute 735412 . Express the result as a common...Ch. 15 - Compute 4.8911.34 .Ch. 15 - Write 0.275 as a common fraction.Ch. 15 - Evaluate 734(916+212) .Ch. 15 - The feed on a lathe is set for 164 inch. How many...Ch. 15 - The following problems have either whole number...Ch. 15 - The following problems have either whole number...Ch. 15 - The following problems have either whole number...Ch. 15 - The following problems have either whole number...
Ch. 15 - The following problems have either whole number...Ch. 15 - The following problems have either whole number...Ch. 15 - The following problems have either whole number...Ch. 15 - The following problems have either whole number...Ch. 15 - The following problems have either whole number...Ch. 15 - The following problems have whole number square...Ch. 15 - Prob. 17ACh. 15 - Prob. 18ACh. 15 - Prob. 19ACh. 15 - The following problems have square roots that are...Ch. 15 - Prob. 21ACh. 15 - Prob. 22ACh. 15 - Prob. 23ACh. 15 - Prob. 24ACh. 15 - Prob. 25ACh. 15 - Prob. 26ACh. 15 - The following problems have square roots that are...Ch. 15 - Prob. 28ACh. 15 - Prob. 29ACh. 15 - Prob. 30ACh. 15 - Prob. 31ACh. 15 - Determine the following numbers with fractional...Ch. 15 - Prob. 33ACh. 15 - Prob. 34ACh. 15 - Prob. 35ACh. 15 - Prob. 36ACh. 15 - Prob. 37ACh. 15 - Prob. 38ACh. 15 - Prob. 39A
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