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 Pell-type sequence of the form (3-sqrt(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 2013-08-25 07:40:41