3. Use the Division Algorithm to establish the following:2-4 (a) The square of any integer is either of the form 3k or 3k +. 1."B()+1=(b) The cube of any integer has one of the forms: 9k, 9k + 1, or 9k + 8.e H.W (a) → youAsS © The fourth power of any integer is either of the form 5k or 5k + 1. e b=5 (d)3=9) 3(3)

(a) Consider the given information. If we divide any integer then the remainder will be 0,1, and 3.…

3. Use the Division Algorithm to establish the following: 4 (a) The square of any integer is either of the form 3k or 3k +1. 3 =4 1%=(b) The cube of any integer has one of the forms: 9k, 9k + 1, or 9k + 8.e ass © The fourth power of any integer is either of the form 5k or 5k +1.e

3. Use the Division Algorithm to establish the following: 4 (a) The square of any integer is either of the form 3k or 3k +1. 3 =4 1%=(b) The cube of any integer has one of the forms: 9k, 9k + 1, or 9k + 8.e ass © The fourth power of any integer is either of the form 5k or 5k +1.e

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 32E

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Question

3. Use the Division Algorithm to establish the following:
2-4 (a) The square of any integer is either of the form 3k or 3k +. 1."
B()+1=(b) The cube of any integer has one of the forms: 9k, 9k + 1, or 9k + 8.e H.W (a) → you
AsS © The fourth power of any integer is either of the form 5k or 5k + 1. e b=5 (d)
3=9) 3(3)

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