Question

use Euclid division Lemma to show that the cube of any positive integer is either of the form 9 M ,9 M + 1 ,9m+ 8 for some integer cube

Answer 1

A positive integer is 9 .
It's cube is 729.
it can also be written as 9 x ( 81 )
I.e. 9 x ( m )

Another positive integer is 5
It's cube is 125
it can also be written as 9 x ( 13 ) + 8
I.e. 9 x ( m ) +8

Similarly another positive integer is 7
It's cube is 343
it can also be written as 9 x ( 39 ) + 1
I.e. 9 x ( m ) + 1

Answer 2

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