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(b) 13|3"+2 + 42n+1 (c) 27 | 25n+1 + 5"+2.

(b) 13|3"+2 + 42n+1 (c) 27 | 25n+1 + 5"+2.

Advanced Engineering Mathematics
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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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
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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