Question

use euclids division lemma to show that the cube of any positive integers is of the form 9m,9m+1 or 9m+8​

Answer 1

Answer:

Step-by-step explanation:

Let,

a=bq+r

Let b=3

=>a=3q, 3q+1, 3q+2 be any integer

a³=(3q)³=27q³=9(3q³),

Where 3q³ =m and m is some integer

And this is in the form of 9m.

2)

a³=(3q+1)³=27q³+27q²+9q+1

=>9(3q³+3q²+q)+1=9m+1,

Where m=3q³+3q²+q

3)

a³=(3q+2)³=27q³+54q²+36q+8

=>9(3q³+6q²+4q)+8=9m+8

Where m=3q³+6q²+4q

Hence proved

Answer 2

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