Question

Use Euclid division lemma to show that the cube of any positive integer is either of the form 8m or 8m+1 or 8m+3 or 8m+5 or 8m+7 where m is a whole number

Answer 1

Let a be any integer in the form of 8q+ r
Where 0<=r<8, so r can be 0,1,2,3,4,5,6,7
* if r be 0 then