SOLUTION: For any positive integer 'n' prove that 'n3-n' is divisible by 6.

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Question 747469: For any positive integer 'n' prove that 'n3-n' is divisible by 6.
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
not true:
n=1
n^3-n=0
Maybe you mean if n is 2 or greater?
%0D%0A%0D%0An%5E3-n=%28n%29%28n%5E2-1%29=%28n-1%29%28n%29%28n%2B1%29%0D%0A

now for
n%3E=2
this product will include 3 consecutive numbers and that means at least one of them will be even and exactly one will be a multiple of 3. Therefore each will be a multiple of 6.


:)