Question

3. Use the Division Algorithm to establish the following: (a) The square of any integer is either of the form 3k or 3k + 1. (b) The cube of any integer has one of the forms: 9k, 9k + 1, or 9k + 8. (c) The fourth power of any integer is either of the form 5k or 5k + 1. 4. Prove that 3a^2 - 1 is never a perfect square. [Hint: Problem 3(a).]

          3. Use the Division Algorithm to establish the following:
(a) The square of any integer is either of the form 3k or 3k + 1.
(b) The cube of any integer has one of the forms: 9k, 9k + 1, or 9k + 8.
(c) The fourth power of any integer is either of the form 5k or 5k + 1.
4. Prove that 3a^2 - 1 is never a perfect square.
[Hint: Problem 3(a).]

3. Use the Division Algorithm to establish the following:
(a) The square of any integer is either of the form 3k or 3k + 1.
(b) The cube of any integer has one of the forms: 9k, 9k + 1, or 9k + 8.
(c) The fourth power of any integer is either of the form 5k or 5k + 1.
4. Prove that 3a^2 - 1 is never a perfect square.
[Hint: Problem 3(a).]

Added by Melissa V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Qbs Educator

04/13/2022

Step 1

For part (a), we consider the remainders when an integer is divided by 3. Show more…

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Use the Division Algorithm to establish the following: (a) The square of any integer is either of the form 3k or 3k + 1. (b) The cube of any integer has one of the forms: 9k, 9k + 1, or 9k + 8. (c) The fourth power of any integer is either of the form 5k or 5k + 1. 4. Prove that 3a^2 - 1 is never a perfect square. [Hint: Problem 3(a).]