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
re: much of a problem even with a computer by broll)
No idea.
However, there may be a recurrence such that y = (3sqrt(7))^(24n+m)+(3+sqrt(7))^(24n+m) has the same final digit for all {m, n}; though I certainly haven't attempted an exhaustive check.
If so, since 2004 = 24*83+12, it will have the same last digit as y = (3sqrt(7))^(12)+(3+sqrt(7))^(12)  a more manageable 1048723328.
Still a stretch for P&P though.

Posted by broll
on 20130825 12:36:13 