Let \(n\) be a positive integer and let \(k\) be the number of positive integers less than \(2^n\) that are invertible modulo \(2^n\). If \(2^n=3\) (mod 13), then what is the remainder when \(k\) is divided by 13?
Turns out the answer is 8.
2^n mod 13 ==3
n ==4 and k==15
15 mod 13 == 2
