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

Tricky question must answer in tricky way.

The question mentions we do not need calculator to compute and we do not need computer to compute too.

The answer is 3.  Can anyone prove that it is wrong?  If nobody can prove that it is wrong, the answer must be 3.

Thanks.

Edited on April 26, 2005, 11:27 pm

Posted by Jonathan Chang on 2005-04-26 23:25:05