compute the remainder when 2^(2^17) + 1 = 19
that + 1 is really throwing me off... I don't know how to deal with it.
I assume you want to find the remainder of modulo .
By the division algorithm we can write where .
But then, .
To find the remainder we need to simplify modulo .
First, .
Multiply both sides by seven to get, .
Therefore, .
Now, by Fermat's little theorem.
Since we see that .
But this is remainder of only if you want to find remainder of just add 1.