What is the 1000th digit to the right of the decimal point in the decimal representation of (1+√2)^3000?

This problem can be solved by algebra alone, without the need for computers or calculators

(In reply to re: Here Jonathan! by Hugo)

MIRACL calc seems a little quirky. The following works the way expected:

1+3= gives 4

and then

*5= gives 20,

taking the previous answer as the first argument to the multiplication.

But

1+2sqr= gives the evaluation of 1+sqrt(2)

but then

^3000= gives some weird short answer, even when the digits are set to say 7000.

In order to get this to work correctly, I had to

1+2sqr=Min, to put it into memory

and then

MR^3000= gives the answer Jer found.

Posted by Charlie on 2005-04-27 20:23:45