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(d))For all integers a, b, and c, if a | b or a c, then a | bc (e) For all integers a, b, and c, if a | b and a c, then a? | bc (f) ) For all integers a, b, and c, if a | bc, then a |b or a | c.

(d))For all integers a, b, and c, if a | b or a c, then a | bc (e) For all integers a, b, and c, if a | b and a c, then a? | bc (f) ) For all integers a, b, and c, if a | bc, then a |b or a | c.

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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Only need part(d) and part(f). Thank you for the help!

Exercise 9.1.6: Proving divisibility statements. Prove or disprove each of the following statements. (a) For all integers a, b, and c, if a | b and a c, then a | (b + c) (b) For all integers a, b, and c, if a | b or a c, then a | (b + c) (c) For all integers a, b, and c, if a | b and a | c, then a | bc (d)) For all integers a, b, and c, if a | b or a c, then a | bc (e) For all integers a, b, and c, if a | b and a c, then a2 | bc (f) For all integers a, b, and c, if a | bc, then a b or a c.
Transcribed Image Text:Exercise 9.1.6: Proving divisibility statements. Prove or disprove each of the following statements. (a) For all integers a, b, and c, if a | b and a c, then a | (b + c) (b) For all integers a, b, and c, if a | b or a c, then a | (b + c) (c) For all integers a, b, and c, if a | b and a | c, then a | bc (d)) For all integers a, b, and c, if a | b or a c, then a | bc (e) For all integers a, b, and c, if a | b and a c, then a2 | bc (f) For all integers a, b, and c, if a | bc, then a b or a c.
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