11. Find all integers x and y, 0< x, y < n, that satisfy each of the following pairs of congruences. If no x, y exist, explain why not. (a) [BB] 2x + y = 1 (mod n) n = 6 x +3y = 3 (mod n) (b) [BB] x+5y = 3 (mod n) 4x +5y = 1 (mod n) n = 9 (c) x+5y = 3 (mod n) 4x +5y = 1 (mod n) n = 8 (d) 7x + 2y = 3 (mod n) 9x + 4y = 6 (mod n) n = 15 II (e) 3x +5y = 14 (mod n) 5x +9y = 6 (mod n) n = 28
11. Find all integers x and y, 0< x, y < n, that satisfy each of the following pairs of congruences. If no x, y exist, explain why not. (a) [BB] 2x + y = 1 (mod n) n = 6 x +3y = 3 (mod n) (b) [BB] x+5y = 3 (mod n) 4x +5y = 1 (mod n) n = 9 (c) x+5y = 3 (mod n) 4x +5y = 1 (mod n) n = 8 (d) 7x + 2y = 3 (mod n) 9x + 4y = 6 (mod n) n = 15 II (e) 3x +5y = 14 (mod n) 5x +9y = 6 (mod n) n = 28
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Q11 c and e
![11. Find all integers x and y, 0 < x, y < n, that satisfy each
of the following pairs of congruences. If no x, y exist,
explain why not.
(a) [BB] 2x + y = 1 (mod n)
n = 6
%3D
x +3y = 3 (mod n)
(b) [BB] x+5y = 3 (mod n)
4x +5y = 1 (mod n)
n =9
%3D
(c) x +5y = 3 (mod n)
4x+5y
n = 8
%3D
= 1 (mod n)
(d) 7x +2y = 3 (mod n)
9x +4y = 6 (mod n)
n = 15
(e) 3x +5y = 14 (mod n)
5x + 9y = 6 (mod n)
n = 28](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02826f83-a729-44a9-a635-628f496d14c7%2F6eb696a4-1b08-44d4-919d-f3df35d4db3d%2Fo02s23m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11. Find all integers x and y, 0 < x, y < n, that satisfy each
of the following pairs of congruences. If no x, y exist,
explain why not.
(a) [BB] 2x + y = 1 (mod n)
n = 6
%3D
x +3y = 3 (mod n)
(b) [BB] x+5y = 3 (mod n)
4x +5y = 1 (mod n)
n =9
%3D
(c) x +5y = 3 (mod n)
4x+5y
n = 8
%3D
= 1 (mod n)
(d) 7x +2y = 3 (mod n)
9x +4y = 6 (mod n)
n = 15
(e) 3x +5y = 14 (mod n)
5x + 9y = 6 (mod n)
n = 28
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