(b) 13|3"+2 + 42n+1 (c) 27 | 25n+1 + 5"+2.
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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Number 6
![L 2010-2 X
A2005-2 X
Offices x
(100) E X
my.cha x
M (EXTEF X
b My Qu X
O HW07 X
* David X
b Passw X
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THE THEORY OF CONGRUENCES
69
6. For n > 1, use congruence theory to establish each of the following divisibility state-
ments:
(a) 7|52n +3 . 25n-2.
(b) 13|3"+2 + 42n+1.
(c) 27 | 25n+1 + 5"+2.
(d) 43 16"+2 + 72n+1.
7. For n > 1, show that
(-13)"+l = (-13)" + (–13)"-! (mod 181)
[Hint: Notice that (-13)2 = -13 + 1 (mod 181); use induction on n.]
8. Prove the assertions below:
(a) If a is an odd integer, then a = 1 (mod 8).
71.
- -- -- J7)
日 OL](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F048faa6b-a100-4249-8bc6-0274c2c51311%2Fd51e9155-1648-47a3-8812-750f0d8d556a%2Fkwh86y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:L 2010-2 X
A2005-2 X
Offices x
(100) E X
my.cha x
M (EXTEF X
b My Qu X
O HW07 X
* David X
b Passw X
Ô https://www.dropbox.com/recents? tk=web_left_nav_bar&preview=David+M. +Burton+-+Elementary+number+theory+(2002%2C+McGraw-Hi... to
Download
Z Open v
E Workflows v
1 Share
THE THEORY OF CONGRUENCES
69
6. For n > 1, use congruence theory to establish each of the following divisibility state-
ments:
(a) 7|52n +3 . 25n-2.
(b) 13|3"+2 + 42n+1.
(c) 27 | 25n+1 + 5"+2.
(d) 43 16"+2 + 72n+1.
7. For n > 1, show that
(-13)"+l = (-13)" + (–13)"-! (mod 181)
[Hint: Notice that (-13)2 = -13 + 1 (mod 181); use induction on n.]
8. Prove the assertions below:
(a) If a is an odd integer, then a = 1 (mod 8).
71.
- -- -- J7)
日 OL
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