19. Establish each of the assertions below: (a) If a is an arbitrary integer, then 6|a(a² + 11). (b) If a is an odd integer, then 24 | a(a² – 1). - [Hint: The square of an odd integer is of the form 8k + 1.] (c) If a and b are odd integers, then 8|(a² – b²). (d) If a is an integer not divisible by 2 or 3, then 24 | (a² + 23). (e) If a is an arbitrary integer, then 360 | a² (a² – 1)(a² – 4).
19. Establish each of the assertions below: (a) If a is an arbitrary integer, then 6|a(a² + 11). (b) If a is an odd integer, then 24 | a(a² – 1). - [Hint: The square of an odd integer is of the form 8k + 1.] (c) If a and b are odd integers, then 8|(a² – b²). (d) If a is an integer not divisible by 2 or 3, then 24 | (a² + 23). (e) If a is an arbitrary integer, then 360 | a² (a² – 1)(a² – 4).
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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![19. Establish each of the assertions below:
(a) If a is an arbitrary integer, then 6|a(a² + 11).
(b) If a is an odd integer, then 24 | a(a² – 1).
-
[Hint: The square of an odd integer is of the form 8k + 1.]
(c) If a and b are odd integers, then 8|(a² – b²).
(d) If a is an integer not divisible by 2 or 3, then 24 | (a² + 23).
(e) If a is an arbitrary integer, then 360 | a² (a² – 1)(a² – 4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf7f73a4-246e-4c35-8f96-56bf14bc4c1c%2F9d590a60-1eb6-4551-b138-85ef261724bd%2F6khcxqa_processed.png&w=3840&q=75)
Transcribed Image Text:19. Establish each of the assertions below:
(a) If a is an arbitrary integer, then 6|a(a² + 11).
(b) If a is an odd integer, then 24 | a(a² – 1).
-
[Hint: The square of an odd integer is of the form 8k + 1.]
(c) If a and b are odd integers, then 8|(a² – b²).
(d) If a is an integer not divisible by 2 or 3, then 24 | (a² + 23).
(e) If a is an arbitrary integer, then 360 | a² (a² – 1)(a² – 4).
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