Determine the digit immediately to the left of the decimal point in the base ten representation of (3+√7)^{2004}
**** For an extra challenge, solve this puzzle using only pen and paper.
(In reply to
much of a problem even with a computer by Charlie)
Charlie, the answer is indeed 7.
Thinking of it as a Pelltype sequence of the form (3sqrt(7))^n+(3+sqrt(7))^n, less a tiny amount, when n= 2004, Wolfram Alpha reports: 28208181083865721...619810417017312247808 (many digits omitted) so the required digit is a 7. The following 903 digits will all be 9's, as you note.
Edited on August 25, 2013, 7:51 am

Posted by broll
on 20130825 07:40:41 