1,2 Question 1For all integers a, b, and c, if a | b and a | c, then a2 | bcO TrueO FalseQuestion 2Compute each quantity below using the methods outlined in this section. Remember that you shouldnot use a calculator.468 mod 702040601

Answered: Question 1 For all integers a, b, and…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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1,2

Question 1
For all integers a, b, and c, if a | b and a | c, then a2 | bc
O True
O False
Question 2
Compute each quantity below using the methods outlined in this section. Remember that you should
not use a calculator.
468 mod 7
02
04
06
01

Expert Solution

Step 1

Question 1: The statement is true.

Proof: Since a | b, there exists an integer k1 such that b = k1a. Similarly, since a | c, there exists an integer k2 such that c = k2a. Therefore, we have:

bc = (k1a)(k2a) = k1k2*(a^2)

Since k1 and k2 are integers, k1*k2 is also an integer. Thus, we have shown that a^2 | bc.

Therefore, the statement is true.

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