Question 0.4. Which integers divide zero? Which are divisible by zero?
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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![Definition 0.1. Let a and b be two integers. We say that a divides b if there is an integer
q so that b = aq. We will use the notation alb as shorthand for this property.
Proposition 0.2. Let a, b, and c be integers. If a|b and ale then a|(b+ c).
Proposition 0.3. Let a, b, and c be integers. If alb then albc.
Question 0.4. Which integers divide zero? Which are divisible by zero?
Proposition 0.5. Let a, b, and c be integers. If alb and alc then a|(b – c).
Question 0.6. Which integers divide one? Which are divisible by one?
Proposition 0.7. Let a, b, c, s and t be integers. If alb and alc then a|(sb+ tc).
Proposition 0.8. Let a, b, and c be integers. If a|b and b|c then alc.
Question 0.9. Does 2|4? Does 2|3? How can you prove your answers?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69a98968-5f96-40b4-b8f7-c8cceea98cdb%2Ff0f5e6b3-90cb-446c-ac76-5ec0d01d1e09%2F6c8flr_processed.png&w=3840&q=75)
Transcribed Image Text:Definition 0.1. Let a and b be two integers. We say that a divides b if there is an integer
q so that b = aq. We will use the notation alb as shorthand for this property.
Proposition 0.2. Let a, b, and c be integers. If a|b and ale then a|(b+ c).
Proposition 0.3. Let a, b, and c be integers. If alb then albc.
Question 0.4. Which integers divide zero? Which are divisible by zero?
Proposition 0.5. Let a, b, and c be integers. If alb and alc then a|(b – c).
Question 0.6. Which integers divide one? Which are divisible by one?
Proposition 0.7. Let a, b, c, s and t be integers. If alb and alc then a|(sb+ tc).
Proposition 0.8. Let a, b, and c be integers. If a|b and b|c then alc.
Question 0.9. Does 2|4? Does 2|3? How can you prove your answers?
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