Question

use Euclid division Lemma to show that the cube of any positive integer is of the form 7 M or 7 M + 1 or 7 + 6​

Answer 1

let 'a' any +ve integer and b=7

apply Euclid's division lemma

a=bq+r , 0 <= r< b

a=3q+r, 0<=r <7

therefore r= 0,1,2,3,4,5,6