1. The problem statement, all variables and given/known data In this statement find the integer y such that x == y mod(n) where 0 =< y < n x=2^71 n=23 2. Relevant equations Let p be a prime number and let a be an integer which is not divisible by p. Then a^(p-1) == 1mod(p) 3. The attempt at a solution I am really struggling as to where to start out with this as obviously 2^71 is too large a number to show fully on any normal or scientific calculator(something like 2.361... x 10^21) and so when dividing by 23 this merely gives 1.0266... x 10^20 which doesn't allow you to find a remainder. I'm not sure if the above equation using p as a prime number is of any relevance, but this would suggest that a^22 ==1mod(23). But i don't know where to go from there, if I can use it at all.