9. Find all integers x, 0 < x < n, satisfying each of the fol- lowing congruences mod n. If no such x exists, explain why not. (a) [BB] 3x = 4 (mod n), n = 6 (b) 4x = 2 (mod n), n = 6 (c) 4x = 3 (mod n), n = 7 (d) 4x = 3 (mod n), n = 6 (e) [BB] 2x = 18 (mod n), n = 50 (f) [BB] 5x =1 (mod n), n = 11 (g) 5x =5 (mod n), n = 25 (h) 4x = 301 (mod n), n = 592 (i) 65x = 27 (mod n), n = 169 (j) 4x = 320 (mod n), n = 592 (k) [BB] 16x = 301 (mod n), n = 595 (1) 79x = 15 (mod n), n =722 (m) 155x = 1185 (mod n), n = 1404
9. Find all integers x, 0 < x < n, satisfying each of the fol- lowing congruences mod n. If no such x exists, explain why not. (a) [BB] 3x = 4 (mod n), n = 6 (b) 4x = 2 (mod n), n = 6 (c) 4x = 3 (mod n), n = 7 (d) 4x = 3 (mod n), n = 6 (e) [BB] 2x = 18 (mod n), n = 50 (f) [BB] 5x =1 (mod n), n = 11 (g) 5x =5 (mod n), n = 25 (h) 4x = 301 (mod n), n = 592 (i) 65x = 27 (mod n), n = 169 (j) 4x = 320 (mod n), n = 592 (k) [BB] 16x = 301 (mod n), n = 595 (1) 79x = 15 (mod n), n =722 (m) 155x = 1185 (mod n), n = 1404
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Q9 d and g
![9. Find all integers x, 0 < x <n, satisfying each of the fol-
lowing congruences mod n. If no such x exists, explain
why not.
(a) [BB] 3x = 4 (mod n), n = 6
(b) 4x = 2 (mod n), n = 6
%3D
%3D
(c) 4x = 3 (mod n), n =7
(d) 4x = 3 (mod n), n = 6
(e) [BB] 2x = 18 (mod n), n = 50
%3D
(f) [BB] 5x = 1 (mod n), n = 11
(g) 5x =5 (mod n), n = 25
(h) 4x = 301 (mod n), n = 592
%3D
(i) 65x = 27 (mod n), n = 169
%3D
(i)4
4x = 320 (mod n), n = 592
(k) [BB] 16x = 301 (mod n), n = 595
79x = 15 (mod n), n = 722
(m) 155x = 1185 (mod n), n = 1404
||
(1)
%3D
%3D
(n) 58x = 6 (mod n), n = 78
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0ee69af-f492-41d4-922e-7766df149334%2F705b8a99-9c3d-48a6-bcb7-c3bef66ad396%2F9wwgzf5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9. Find all integers x, 0 < x <n, satisfying each of the fol-
lowing congruences mod n. If no such x exists, explain
why not.
(a) [BB] 3x = 4 (mod n), n = 6
(b) 4x = 2 (mod n), n = 6
%3D
%3D
(c) 4x = 3 (mod n), n =7
(d) 4x = 3 (mod n), n = 6
(e) [BB] 2x = 18 (mod n), n = 50
%3D
(f) [BB] 5x = 1 (mod n), n = 11
(g) 5x =5 (mod n), n = 25
(h) 4x = 301 (mod n), n = 592
%3D
(i) 65x = 27 (mod n), n = 169
%3D
(i)4
4x = 320 (mod n), n = 592
(k) [BB] 16x = 301 (mod n), n = 595
79x = 15 (mod n), n = 722
(m) 155x = 1185 (mod n), n = 1404
||
(1)
%3D
%3D
(n) 58x = 6 (mod n), n = 78
%3D
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