Hello,

If you can work with modular arithmetic, then you're done.

You have to prove that there is no k such that

Fermat's little theorem tells us that

so consider the possible values of k modulo 6 :

etc....

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- Apr 19th 2009, 09:41 AM #1

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- Apr 19th 2009, 09:49 AM #2

- Apr 19th 2009, 09:54 AM #3
As you say, we will try to find a contradiction. First note that

The fact that implies since

Now implies thus and then ( In general we have that if and only if )

We then write that is which is not possible since and so (expand using the binomial theorem)

- Apr 20th 2009, 02:03 AM #4

- Apr 21st 2009, 02:48 AM #5