   Chapter 8.1, Problem 90ES Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584

Solutions

Chapter
Section Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584
Textbook Problem

Modular division can be performed by considering the related multiplication problem. For instance, if 5 ÷ 7 = x , then x ⋅ 7 = 5 . Similarly, the quotient ( 5 ÷ 7 ) mod 8 is the solution to the congruence equation x ⋅ 7 ≡ 5 mod 8 , which is 3. Find the given quotient. ( 4 ÷ 5 ) mod 8

To determine

To calculate: To find the quotient of (4÷5)mod8

Explanation

Given information: Expression (4÷5)mod8 is given

Calculation:

Consider the following expression (4÷5)mod8

The quotient of the above expression is the solution of the congruence equation x54mod8

Now solve the equation x54mod8

Begin with 0; substitute each whole number less than 8 into the congruence equation to get

x=05(0)4mod8 not a solution x=15(1)4mod8 not a solution x=25(2)4mod8 not a solution x

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