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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
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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Pls. answer number 1, 2, 3.

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.
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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