SOLUTION: What is the largest intger that n^3-n is divisable by k for all postive intgers n?

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Question 34218: What is the largest intger that n^3-n is divisable by k for all postive intgers n?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
THE QUESTION IS NOT VERY CLEAR ..
IF IT REALLY MEANS WHAT IS WRITTEN THEN SINCE N IS AN INTEGER N^3-N IS AN INTEGER AND IT IS DIVISIBLE BY N^3-N WHICH IS THE LARGEST INTEGER.IF IT IS NEEDE TO FIND A NUMBER LESS THAN THIS THEN
N^3-N=N(N^2-1)=N(N+1)(N-1)...SO TAKING THE LARGER OF THE 3 FACTORS N(N+1)=N^2+N IS THE LARGEST INTEGER FOR ALL N.