Math 3) (i) Prove that every perfect square is either a multiple of 4 orone more than a multiple of 4. [Hint: Every positive integer is of oneof the following forms: 4 k, 4 k+ 1, 4 k+ 2, 4k+3. Considerthe squares of numbers of each of these types.](ii)Prove that no number of the form 4 k + 3 (where k is a positiveinteger) can ever be the sum of two perfect squares. [Hint: Use part(i) 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.]

(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.]

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 32EQ

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