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

As modular arithmetic allows that taking a power can be accomplished one step at a time, multiplying my the number whose power is taken and reducing by the modulus, as many times as needed per the definition of a power, we can raise 1024 (which is 2^10) to the 199 power mod 1990 one step at a time:
1024^2 mod 1990 = 1836. Then 1836 * 1024 mod 1990 = 1504, which is therefore 1024^3 mod 1990. Continue that process another 196 times to get 1024^199 mod 1990, which is 2^1990 mod 1990.

Posted by Charlie on 2003-03-02 09:32:32