Question

Use Euclid's division Lemma to show that the cube of any positive integer is either of
the form 9m, 9m + 1 or, 9m + 8 for some integer m.I have the solution but have a doubt in it.....
solution.....Let x be any positive integer. Then, it is of the form 3q or, 3q +1 or, 3q + 2. So, we
have the following cases.....and so on.......
Those who know the answer for it, please tell me where Euclid's division lemma has been used here?​

Answer 1

Answer:

a=bq+r (Euclid division lemma). any no divisible by 9 is also divisible by 3 so we will take b=3 therefore r=0,1,2 when r=0 then it would be 3q+0=3q now by doing cube of (3q) we will get 27q raise to the power 3 then we will take 9 as common resulting in 9(3qraise to the power3) then we will write it in the form 9m and so on......