I need help on proving such that no integer k exists.

I assume the to proof this I need to use contradiction, assume there is some k such that . But Im having trouble finding a contradiction.

Please help,

Thanks

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

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

- April 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)

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

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