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Topic: .. pOwers of a real number
Replies: 12   Last Post: Jun 25, 2009 3:59 AM

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 galathaea Posts: 1,646 Registered: 7/2/05
Re: .. pOwers of a real number
Posted: Jun 24, 2009 7:44 PM

On Jun 24, 3:58 pm, qsymmetry <qsymme...@email.com> wrote:
> If x is a real number other than 0, 1, -1, is it true
> that all the powers of x are distinct?
>
> If  for some  integers r =/= s  we have   x^r = x^s,
> then x^{r - s} = 1.
>
> If r  - s  is even, then x = 1, or -1;  if r - s is odd,
> then x = 1.
>
> But I don't see a contradiction yet..
>
> Any thoughts on this would be appreciated.

you missed all the other roots of unity

and generally
x^r = x^(r + 2 pi n i)
with n an integer

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galathaea: prankster, fablist, magician, liar

Date Subject Author
6/24/09 qsymmetry
6/24/09 ab
6/24/09 galathaea
6/24/09 ab
6/24/09 galathaea
6/24/09 ab
6/24/09 rgvickson@gmail.com
6/25/09 William Elliot
6/24/09 rgvickson@gmail.com
6/24/09 galathaea
6/24/09 ab
6/24/09 Guest
6/25/09 PianoMan