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#1 2008-03-20 07:07:23
- tony123
- Full Member
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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
- Legendary Member
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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)
#3 2008-03-24 00:43:35
- Kurre
- Power Member
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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)
