Any idea how to solve the equation 78^x = x (mod 10^12) ?
I've looked over every congruence and can't seem to find anything useful.
Let's see... you're looking for a number x such that the last 12 digits of 78^x is the same as the last 12 digits of x.
Perhaps we should start with just the last digit.
Can you solve 78^x = x (mod 10)?