Answered: 4. 5|8" – 3", Vn E N 5. 4|5" – 1, Vn E… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 63RE

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Pls. answer number 4, 5 and 6.

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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