Question

8. A) Use Euclid's division lemma to show that the cube of any positive
integer is of the form 3K or 3K+1 or 3K+8?​

Answer 1

Step-by-step explanation:

Case1

a=3q

Bycubing. a= 27^3

A=3(9q^2). (9q^2 =k)

a=3k

Case 2.

A=(3q+1)^3

A=27^3+27q^2+9q+1

3(9q^3+9q^2+3q)+1. Take (9q^3+9q^2+3q=k)

So, 3k+1

Case3

A=(3q+2)^3

A=27^3+18q^2+12q+8

A=3(9q^3+6q^2+4q+2)+2.Take(9q^3+6q^2+4q=K)

) A=3K+2

So, cube of any positive

cube of any positiveinteger is of the form 3K or 3K+1 or 3K+8

Hope this will help you

Mark it brainliest