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## #1 2008-03-20 07:07:23

tony123
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### Determine all real x

Determine all real x

such that

is an integer for any integer n.

## #2 2008-03-20 08:07:15

JaneFairfax
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### Re: Determine all real x

Sorry …

I thought I got x = ±1, but my working was wrong.

Last edited by JaneFairfax (2008-03-20 08:20:34)

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #3 2008-03-24 00:43:35

Kurre
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### Re: Determine all real x

assume that x+1/x is an integer. Squaring gives:

which also is an integer
now assume that

are both integers
the following product is an integer:

therefor, x^(n+1) + x^(-n-1) is an integer and by the induction principle it holds for all n.
Hence all x that satisifies the condition is the ones that satisfy that x+1/x is an integer, which implies that there exists infinite many reals satisfying the problems condition.

ps. how do i do the sign, that shows that an element belongs to a set in mathcode?

Last edited by Kurre (2008-03-24 00:45:43)

Daniel123
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Kurre
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Thanks!