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Asked by priyankas | 15th Oct, 2008, 10:01: PM

Expert Answer:

Let n be a positive integer.

Then n = 3p  or 3p + 1 or 3p+ 2

Case I : If n = 3p , then n3 = 27 p 3 = 9m

Case II If n = 3p+1 , then n3 = (2p+1)3 = 27 p3 + 9p ( 3p+1) + 1

 = 9m +1

Case II If n = 3p +2 , the n3 = ( 3p+2) 3 = 27 p3 + 18 p ( (3p + 2 )  + 8 = 9m + 8

Therefore , from Case I , II  and II , n cube of any positive integer is of the form 9m, 9m+1 or 9m+8. 

Answered by  | 16th Oct, 2008, 08:03: PM

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