use euclid division leema to show that the cube of any positive integer is of the form 9m,9m+1or 9m+8
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Answer:let us we suppose a be any positive integer using euclid's divison lemma with b=3
we get a=3q,3q+1,3q+2
where q is a whole number
a3=(3q)3=27q3=9q
where q=3q3
(3q+1)=27q3+27q2+9q+1
=9q+1 where q=3q3+3q2+q
also (3q+2)3=27q3+54q2+36q+8
=9q+8 where q=3q3+6q2+4q
hence the cube of any positive integer is of the form 9q,9q+1,9q+8 for some integer q.
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