Question

use euclid's division Lemma to show that the cube of any positive integers is formm 9 m, 9 m+ 1 or 9 m+ 8​

Answer 1

Answer:

here is your answer

hope this will help you

Answer 2

Answer:

Step-by-step explanation:

Let a be any positive integer and b=9

By euclid's division lemma

a=bq+r

a=9q+r

(0 is greater than equal to r which is greater than 9)

( r = 0,1.....8)

For r = 0

(a)cube = (9q)cube. (We r cubing the both sides)

=(729q)cube. (so we get this)

=8(81q cube) (729can be is written like this)

So let 81q cube be =m

=9m (in place of that we r writing it as m)

For r=1

a cube = (9q+1) cube

=729q cube +27q square +27q +1

9(81qcube + 3q square +3q) +1

Let, 81qcube + 3q square + 3q be m

So, 9m+1

For r=8

(a)cube = (9q+8)Cube

=729q cube + 216q square + 216q +512q cube

=729q cube + 216q square + 216q + 501qcube + 8

(writing 512q cube as 501q cube + 8)

9(81qcube + 24q square + 24 q + 56qcube)+8

Let it be m

So we get 9m+8