Given that n is a positive integer, determine the remainder (in terms of n) whenever 3^(2^n) – 1 is divided by 2^(n+3)

Note: (a)^b implies 'a' raised to the power of 'b', ((a)^b)^c implies 'a' raised to the power 'bc', but a^(b^c) implies 'a' raised to the power 'b' raised to the power 'c'

To calculate the remainder, divide the numerator by the denominator and multiply the decimal component of the result by the denominator:

For n=1 to 5 the remainders are:

8
16
32
64
128

Each of those remainders fits the expression 2^(n+2)

Edited on April 20, 2011, 1:58 pm

Posted by Ben Gornall on 2011-04-20 13:50:50