4. For n > 1, use mathematical induction to establish each of the following divisibility statements: (a) 8|52" + 7. [Hint: 520k+1) + 7 = 5?(5% + 7) + (7 – 52 . 7).] (b) 15|24" – 1. (c) 5|33n+1 + 2"+1. (d) 21 |4"+1 + 52n-1. (e) 24 2.7" + 3.5" -5.
4. For n > 1, use mathematical induction to establish each of the following divisibility statements: (a) 8|52" + 7. [Hint: 520k+1) + 7 = 5?(5% + 7) + (7 – 52 . 7).] (b) 15|24" – 1. (c) 5|33n+1 + 2"+1. (d) 21 |4"+1 + 52n-1. (e) 24 2.7" + 3.5" -5.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![4. For n > 1, use mathematical induction to establish each of the following divisibility
statements:
(a) 8|52n + 7.
[Hint: 52(k+1) + 7 = 5?(5k + 7) + (7 – 52 . 7).]
(b) 15|24" – 1.
(c) 5|33n+1 + 2"+1.
(d) 21 |4"+1 + 52n-1.
(e) 24 |2.7" + 3.5" – 5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f2b1484-8577-4471-97bc-754f01bb4bc4%2F722690ff-715c-436c-8f00-d7403b6e68b1%2Flkcd16k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. For n > 1, use mathematical induction to establish each of the following divisibility
statements:
(a) 8|52n + 7.
[Hint: 52(k+1) + 7 = 5?(5k + 7) + (7 – 52 . 7).]
(b) 15|24" – 1.
(c) 5|33n+1 + 2"+1.
(d) 21 |4"+1 + 52n-1.
(e) 24 |2.7" + 3.5" – 5.
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