Use Euclid divisions lemma to show That the cube of any positive integer is of form 9m, 9m+1,or 9m+8

Use Euclid divisions lemma to show That the cube of any positive integ

1.	Use Euclid divisions lemma to show That the cube of any positive integer is of form 9m, 9m+1,or 9m+8
Answer» Let a positivi integer x when divided by 3 gives remainder rThen by using euclids division lemmaX=3q+r. And. r=0,1or2Case 1:-. r=0 X^3= 3×3×3×q×q×q+0×0×0 =27q^3 =9×3q^3 =9m. ( Say 3q^3=m)Similarly in case 2 &3 we find 9m+1 and 9m+8 respectively.