Show that the remainder when 2^1990 (2 to the power of 1990) is divided by 1990 equals 1024.

To prove a remainder, you have to prove that the rest is an integer factor. So:
2^1990/1990 = N R1024
2^1990/1990 = N + 1024/1990
2^199)(2^10)/1990 = N + 2^10/1990
N = (2^199)(2^10)/1990 - 2^10/1990
N = (2^199-1)(2^10)/1990
where you have to prove that N is an integer. That's as far as I have gotten...

Posted by DJ on 2003-03-01 09:45:38