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
Uncle! by McWorter)
I give up, too.
I also have ben playing with David Shin's proof outline, and I have
convinced myself that it was a brilliant idea that doesn't work.
If we are focusing on the positive root of ax^2 + bx + c = 0,
then I believe that a must equal one, in order to ensure that X(n) is
always an even integer.
However, I have ruled out:
a = 1, b even, c even
a = 1, b even, c odd
a = 1, b odd, c even
a = 1, b odd, c odd
I'll be very interested to see the solution. I have also come
around to thinking (despite what SteveH says) that the problem maybe
should be: "Find a positive real number X, such that [X^n] is an
even number whenever n is odd, and [X^n] is an odd number whenever n is even."
Incidentally, SteveH and I are not the same person, not relatives, not
collaborators, and (to the best of my knowledge) not even acquaintances.
re: Uncle!
