Question

use euclid division Lemma to show that cube of any positive integer is either of the form 9 M ( 9 mand + 1) or (9m + 8)

Answer 1

hope this helps you ☺

Answer 2

Hey!

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Let a = 3q + r

a = 3q

•Cube both sides

(a)³ = (3q)³

= (a) = 9q³

Let q³ = m

= 9m

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Let a = 3q + 1

a = 3q + 1

•Cube both sides

(a)³ = (3q + 1)³

(a)³ = 27q³ + 27q² + 9q + 1

•Take 9 as common :-

(a)³ = 9 (3q³ + 3q² + q) + 1

•Let (3q³ + 3q² + q) = m

(a)³ = 9m + 1

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Let a = 3q + 2

Cube both sides

(a)³ = (3q + 2)³

(a)³ = 27q³ + 54q² + 36q + 8

•Take 9 common

(a)³ = 9 (3q³ + 6q² + 4q) + 8

•Let (3q³ + 6q² + 4q) = m

(a)³ = 9m + 8

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Regards :)

Cybary

Be Brainly :)