The following is a question from a set-text that I have chosen to explore.
What digit is imediately to the right of the decimal point in (sqrt(3) + sqrt(2))^2002
The Attempt at a Solution
I have not gone very far with this, and may need to find a different problem. What I have done is explore (sqrt(3) + sqrt(2))^n, for n = 0, 1, 2, 3, 4... and found that for even values of n (which include 2002) that the expression evaluates to the sum of a constant and a constant multiple of sqrt(6). Both constants are too large to calculate.
I also know that [(sqrt(3) + sqrt(2))^2002][(sqrt(3) - sqrt(2))^2002]=1, but I am not sure if that can be used to find a solution.
I am presently exploring [(sqrt(3) + sqrt(2))^2002]-[(sqrt(3) - sqrt(2))^2002] and find that a whole lot of terms are being cancelled.
Any suggestions would be appreciated,