9. Let n e Z. Prove that 3k E Z such that n = 8k or n4 = 8k + 1. In other words, prove that by raising anyinteger to the fourth power, it can be written as a multiple of 8 or a multiple of 8 plus 1. Hint: Read Thm4.4.3 pg 186, and study the author's trick to proving it

We will use the fact that any integer is either even or odd to prove the required result.

Answered: 9. Let n E Z. Prove that 3k EZ such…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .

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9. Let n E Z. Prove that 3k EZ such that n' = 8k or n' = 8k + 1. In other words, prove that by raising any integer to the fourth power, it can be written as a multiple of 8 or a multiple of 8 plus 1. Hint: Read Thm 4.4.3 pg 186, and study the author's trick to proving it