Proving the Largest Natural Number m for Divisibility of n^3-n

  • #51
Digging up something old, but I too was looking through Bartle & Sherbert's Intro to Real Analysis and thought this was interesting so I googled the problem. I am with Alex B on this except for one thing: Technically, for the proof to be correct, one would have to take note of the n=1 case as well. This does turn out to be trivial, in that 1^3 - 1 = 0 is divisible by any number. It's still an important fact to not for correctness though, since we'd be interested in proving this for all Natural numbers.
 

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