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Determine all real xDetermine all real x is an integer for any integer n. #2 20080320 08:07:15
Re: Determine all real xSorry … Last edited by JaneFairfax (20080320 08:20:34) #3 20080324 00:43:35
Re: Determine all real xassume 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^(n1) 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 (20080324 00:45:43) 