Can you please help me with

Prove that n^3-n is divisible by 3

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- December 9th 2009, 12:45 PMwantanswersmathematical induction
Can you please help me with

Prove that n^3-n is divisible by 3 - December 9th 2009, 01:06 PMcraig
for some .

First we see if it holds for

, therefore true for

Now we use what's called the induction step, we assume that it's true for where k is some natural nubmer.

This gives us

We then prove this for , giving us

.

Expanding the brackets gives

which can be written as

.

Therefore it is true for if true for .

You know it is true for 0, therefore true for 1. True for one, therefore true for 2....

Hope this helps