Question

Use Euclid's division lemma to show that the cube of any positive integer is of the form
9m, 9m + 1 or 9m +8.​

Answer 1

Step-by-step explanation:

let a,b are two integer ,b=3

by using Euclid division lemma,a=bq+r

r=0

(a)³=3q(a)³

(a)³ 9(3q)

a=9m

r=1a=3q+r

cubic on both sides

(a)³=(3q+r)¾

=(3q)³+(1)³+3(3q)(1)(3q+1)

27+1+9q(3q+1)

9(3q+1+(3q+1)+1

here(3q+1+(3q+1)+1) is taken as m

so,9m+1

r=2a=3q+2(a)³=(3q+2)³=(3q)³+(2)³+3(3q)(2)(3q+2)

=27+8+18(3q+2)

=9(3q+2q(3q+2))+8

here (3q+2q(3q+2) is taken as m

so,9m+8

Answer 2

Answer:

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