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.

I thought I could prove this indirectly by showing only that X exists, but I got stuck.  Here's why:

By experimentation, X=1.4796 works up to n=10.  However, [X^11]=74; and whenever I tweaked X, either [X^11] remained even or [X^k], for some k<11, slipped into the wrong parity.  This problem is looking better and better.

Posted by McWorter on 2005-02-28 13:04:01