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# (-1)^n watch

1. Something that just popped into my mind...does there exist an such that:
?
Could someone come up with a a proof that either confirms or refutes this?
2. so far as n is a whole number and not a fraction - you should always get real numbers
3. n = 1/3
4. (k an integer)

For this to be real, we need (m an integer)

Therefore n is rational. (Specifically a rational of the form )
5. (Original post by SimonM)
(k an integer)

For this to be real, we need (m an integer)

Therefore n is rational. (Specifically a rational of the form )
So basically as long as the denominator is odd it'll work. Nice proof by the way!
6. For and we define , which real only when for some . Can this happen when and ? [Bear in mind that the interval on which you can choose arg z to lie is arbitrary.]

(Original post by imzir)
so far as n is a whole number and not a fraction - you should always get real numbers
(Original post by Bobifier)
n = 1/3
The OP said that , so neither whole numbers nor 1/3 are suitable choices for n here.
7. So in answer to my question, no. Thanks for clarifying that.
8. (Original post by nuodai)
The OP said that , so neither whole numbers nor 1/3 are suitable choices for n here.
I realised that as I posted, and at the time I'm sure I meant to delete it, but somehow it didn't quite seem to come to anything...

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