In rs Aggarwal book of new addition question for any positive integer n prove that ncube - n is divisible by 6
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Let n be any positive integer.
On dividing n by 6,then q as quotient and r as remainder
Let n=6q+r,(r=0,1,2,3,4,5)
Case1=when r=0
(n)3-n=(6q)3-6q. (q is an integer)
=(216q)3-6q
=6{(36q)3-q}
=6m. (m is an integer)
On dividing n by 6,then q as quotient and r as remainder
Let n=6q+r,(r=0,1,2,3,4,5)
Case1=when r=0
(n)3-n=(6q)3-6q. (q is an integer)
=(216q)3-6q
=6{(36q)3-q}
=6m. (m is an integer)
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