1. a|b iff ac\bc, where c # 0. 2. If alc and a+ b= c, then a|b. 3. 7|23n – 1, Vn € N -
1. a|b iff ac\bc, where c # 0. 2. If alc and a+ b= c, then a|b. 3. 7|23n – 1, Vn € N -
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
Pls. answer number 1, 2, 3.
Transcribed Image Text:Prove the following.
1. alb iff ac bc, where c + 0.
2. If alc and a+ b = c, then a|b.
3. 7|23n – 1, Vn € N
-
4. 5|8" – 3", Vn E N
5. 4|5" – 1, Vn E N
6. 3|n(n+ 1)(n +2), Vn E N
7. 6|n(n+ 1)(n+ 2), Vn E N
8. If a and b are odd integers, then 8|(a² – b²).
9. If 5|(2a + 1) for some integer a, then 25|(14a² + 19a – 19).
10. The square of any integers is of the form 5k, 5k + 1 or 5k + 4.
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