Determine all real x

tony123 · 2008-03-19 08:07:23

such that

is an integer for any integer n.

JaneFairfax · 2008-03-19 09:07:15

Sorry

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

Last edited by JaneFairfax (2008-03-19 09:20:34)

Kurre · 2008-03-23 01:43:35

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 (2008-03-23 01:45:43)

Daniel123 · 2008-03-23 02:00:40

Kurre · 2008-03-23 02:06:43

Thanks!

Math Is Fun Forum

#1 2008-03-19 08:07:23

Determine all real x

#2 2008-03-19 09:07:15

Re: Determine all real x

#3 2008-03-23 01:43:35

Re: Determine all real x

#4 2008-03-23 02:00:40

Re: Determine all real x

#5 2008-03-23 02:06:43

Re: Determine all real x

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