Elementary Differential Equations
10th Edition
ISBN: 9780470458327
Author: William E. Boyce, Richard C. DiPrima
Publisher: Wiley, John & Sons, Incorporated
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Chapter 4.3, Problem 15P
To determine
The suitable form for
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Students have asked these similar questions
Example: For what odd primes p is 11 a quadratic residue modulo p?
Solution:
This is really asking "when is (11 | p) =1?"
First, 11 = 3 (mod 4). To use LQR, consider two cases p = 1 or 3 (mod 4):
p=1 We have 1 = (11 | p) = (p | 11), so p is a quadratic residue modulo 11. By
brute force:
121, 224, 3² = 9, 4² = 5, 5² = 3 (mod 11)
so the quadratic residues mod 11 are 1,3,4,5,9.
Using CRT for p = 1 (mod 4) & p = 1,3,4,5,9 (mod 11).
p = 1
(mod 4)
&
p = 1
(mod 11
gives p
1
(mod 44).
p = 1
(mod 4)
&
p = 3
(mod 11)
gives p25
(mod 44).
p = 1
(mod 4)
&
p = 4
(mod 11)
gives p=37
(mod 44).
p = 1
(mod 4)
&
p = 5
(mod 11)
gives p
5
(mod 44).
p = 1
(mod 4)
&
p=9
(mod 11)
gives p
9
(mod 44).
So p =1,5,9,25,37 (mod 44).
how to construct the following same table?
please work out more details give the solution.
Chapter 4 Solutions
Elementary Differential Equations
Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - In each of Problems 1 through 6, determine...Ch. 4.1 - Prob. 6PCh. 4.1 - In each of Problems 7 through 10, determine...Ch. 4.1 - Prob. 8PCh. 4.1 - In each of Problems 7 through 10, determine...Ch. 4.1 - Prob. 10P
Ch. 4.1 - In each of Problems 11 through 16, verify that the...Ch. 4.1 - In each of Problems 11 through 16, verify that the...Ch. 4.1 - In each of Problems 11 through 16, verify that the...Ch. 4.1 - In each of Problems 11 through 16, verify that the...Ch. 4.1 - In each of Problems 11 through 16, verify that the...Ch. 4.1 - In each of Problems 11 through 16, verify that the...Ch. 4.1 - Prob. 17PCh. 4.1 - Prob. 18PCh. 4.1 - Prob. 19PCh. 4.1 - Prob. 20PCh. 4.1 - Prob. 21PCh. 4.1 - Prob. 22PCh. 4.1 - Prob. 23PCh. 4.1 - Prob. 24PCh. 4.1 - Prob. 25PCh. 4.1 - Prob. 26PCh. 4.1 - Prob. 27PCh. 4.1 - Prob. 28PCh. 4.2 - In each of Problems 1 through 6, express the given...Ch. 4.2 - In each of Problems 1 through 6, express the given...Ch. 4.2 - In each of Problems 1 through 6, express the given...Ch. 4.2 - In each of Problems 1 through 6, express the given...Ch. 4.2 - In each of Problems 1 through 6, express the given...Ch. 4.2 - In each of Problems 1 through 6, express the given...Ch. 4.2 - Prob. 7PCh. 4.2 - Prob. 8PCh. 4.2 - Prob. 9PCh. 4.2 - Prob. 10PCh. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - Prob. 15PCh. 4.2 - Prob. 16PCh. 4.2 - Prob. 17PCh. 4.2 - Prob. 18PCh. 4.2 - Prob. 19PCh. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 11 through 28, find the...Ch. 4.2 - In each of Problems 29 through 36, find the...Ch. 4.2 - Prob. 31PCh. 4.2 - Prob. 32PCh. 4.2 - Prob. 33PCh. 4.2 - Prob. 34PCh. 4.2 - Prob. 35PCh. 4.2 - Prob. 36PCh. 4.2 - Prob. 37PCh. 4.2 - Prob. 38PCh. 4.2 - Prob. 39PCh. 4.2 - Prob. 40PCh. 4.3 - In each of Problems 1 through 8, determine the...Ch. 4.3 - In each of Problems 1 through 8, determine the...Ch. 4.3 - In each of Problems 1 through 8, determine the...Ch. 4.3 - In each of Problems 1 through 8, determine the...Ch. 4.3 - In each of Problems 1 through 8, determine the...Ch. 4.3 - In each of Problems 1 through 8, determine the...Ch. 4.3 - In each of Problems 1 through 8, determine the...Ch. 4.3 - In each of Problems 1 through 8, determine the...Ch. 4.3 - In each of Problems 9 through 12, find the...Ch. 4.3 - In each of Problems 9 through 12, find the...Ch. 4.3 - In each of Problems 9 through 12, find the...Ch. 4.3 - In each of Problems 9 through 12, find the...Ch. 4.3 - In each of Problems 13 through 18, determine a...Ch. 4.3 - In each of Problems 13 through 18, determine a...Ch. 4.3 - In each of Problems 13 through 18, determine a...Ch. 4.3 - In each of Problems 13 through 18, determine a...Ch. 4.3 - In each of Problems 13 through 18, determine a...Ch. 4.3 - In each of Problems 13 through 18, determine a...Ch. 4.3 - Prob. 19PCh. 4.3 - Show that linear differential operators with...Ch. 4.4 - Prob. 1PCh. 4.4 - In each of Problems 1 through 6, use the method of...Ch. 4.4 - In each of Problems 1 through 6, use the method of...Ch. 4.4 - In each of Problems 1 through 6, use the method of...Ch. 4.4 - In each of Problems 1 through 6, use the method of...Ch. 4.4 - In each of Problems 1 through 6, use the method of...Ch. 4.4 - In each of Problems 7 and 8, find the general...Ch. 4.4 - In each of Problems 7 and 8, find the general...Ch. 4.4 - In each of Problems 9 through 12, find the...Ch. 4.4 - In each of Problems 9 through 12, find the...Ch. 4.4 - In each of Problems 9 through 12, find the...Ch. 4.4 - In each of Problems 9 through 12, find the...Ch. 4.4 - Given that x, x2, and 1/x are solutions of the...Ch. 4.4 - Find a formula involving integrals for a...Ch. 4.4 - Find a formula involving integrals for a...Ch. 4.4 - Find a formula involving integrals for a...Ch. 4.4 - Find a formula involving integrals for a...
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