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.

Shin's solution may be wrong.  With X=1+sqr(3), [X]=2, [X^2]=4, [X^3]=6, etc.

If n is assumed to start with n=1, then X=-.5 (or any number between -1 and 0) works.  [X]=0, [X]=-1, [X^2]=0, [X^3]=-1, etc.  In general [X^n]=0 when n is a positive even integer and [X^n]=-1 when n is an odd positive integer.

Posted by McWorter on 2005-02-25 23:10:46