Question

Use Euclid's division lemma to show that the cube of any positive integer is of the form 9M 9M + 1 or 9M + 8

In this question we consider b=3 .......but why ???
Why we don't take b=9

Answer 1

Here is your answer

Let x be any positive integer

by Euclid Division Lemma

a = bq + r

Put a = x and b = 9

we get 0 < r < b

therefore r = 0 1 2 3....... 8

Now substitute these values to get answer

Thank You