Let [z] mean the Greatest Integer less than or equal to z. Find a positive real number X, such that [X^n] is an even number whenever n is even, and [X^n] is an odd number whenever n is odd.

(In reply to Solution without full spoiler by SteveH)

Ha, ha!  I feel like an idiot!  Shin's proof outline works!  (5+sqrt(33))/2 should also have the desired property.  Let r and s be the roots of x^2-3x-2.  Then all terms r^n+s^n are ODD, for n>0.   Bravo, David!  And kudos, SteveH, for a marvelous problem!

Posted by McWorter on 2005-03-10 05:21:55