(1) Prove that every perfect square is either a multiple of 4 or e more than a multiple of 4. [Hint: Every positive integer is of one the following forms: 4 k, 4 k+ 1, 4k+ 2, 4k+3. Consider e squares of numbers of each of these types.] )Prove that no number of the form 4 k+3 (where k is a positive teger) can ever be the sum of two perfect squares. [Hint: Use part and think about adding any two perfect squares.]
(1) Prove that every perfect square is either a multiple of 4 or e more than a multiple of 4. [Hint: Every positive integer is of one the following forms: 4 k, 4 k+ 1, 4k+ 2, 4k+3. Consider e squares of numbers of each of these types.] )Prove that no number of the form 4 k+3 (where k is a positive teger) can ever be the sum of two perfect squares. [Hint: Use part and think about adding any two perfect squares.]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![3) (i) Prove that every perfect square is either a multiple of 4 or
one more than a multiple of 4. [Hint: Every positive integer is of one
of the following forms: 4 k, 4 k+ 1, 4 k+ 2, 4k+3. Consider
the squares of numbers of each of these types.]
(ii)Prove that no number of the form 4 k + 3 (where k is a positive
integer) can ever be the sum of two perfect squares. [Hint: Use part
(i) and think about adding any two perfect squares.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3046cdee-db5c-45b8-83b1-15e9b585ff09%2F669ecfc8-6a42-47b9-97c0-bde2b9deed9e%2F7mv3ia_processed.png&w=3840&q=75)
Transcribed Image Text:3) (i) Prove that every perfect square is either a multiple of 4 or
one more than a multiple of 4. [Hint: Every positive integer is of one
of the following forms: 4 k, 4 k+ 1, 4 k+ 2, 4k+3. Consider
the squares of numbers of each of these types.]
(ii)Prove that no number of the form 4 k + 3 (where k is a positive
integer) can ever be the sum of two perfect squares. [Hint: Use part
(i) and think about adding any two perfect squares.]
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