I was trying to find all the numbers n for which $2^n=n\mod 10^k$ using Mathematica. My first try:
Reduce[2^n == n, n, Modulus -> 100]
However, I receive the following error:
Reduce::nsmet: This system cannot be solved with the methods available to Reduce. >>
using $n^2$ instead of $2^n$ works just fine, where is the problem with $2^n$?
Ont top of that, how do I keep the modulus $10^k$ variable and therefore, receive a solution dependant on k?