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)