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Give a reason for your answer. Assume that all | Ch 4.3 - 12E

Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp ISBN: 9780495391326 48

Solution for problem 12E Chapter 4.3

Discrete Mathematics with Applications | 4th Edition

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Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp

Discrete Mathematics with Applications | 4th Edition

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Problem 12E

Problem 12E

Give a reason for your answer. Assume that all variables represent integers.

Exercise

If n = 4k + 1, does 8 divide n2 − 1?

Step-by-Step Solution:
Step 1 of 3

Solution:-

Step1

Given that

We have to give a reason for our answer. Let all variables represent integers. We have to If n = 4k + 1, does 8 divide n2 − 1?

Step2

8 divide − 1 :-yes

Using definition of divisibility, if m and e are integers, then m is divisible by e only if m=ec, for some integer c.

Suppose that n=4k+1

Put value of n in − 1 we get

− 1=

          =

          =

         =

Step3

From the definition of divisibility

And  is an integer because k is an integer and sums and product of integers are integers.

Therefore, − 1 is divisible by 8.

Step 2 of 3

Chapter 4.3, Problem 12E is Solved
Step 3 of 3

Textbook: Discrete Mathematics with Applications
Edition: 4
Author: Susanna S. Epp
ISBN: 9780495391326

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Give a reason for your answer. Assume that all | Ch 4.3 - 12E