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 dependent on k?

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 $2^n\;$?

On top of that, how do I keep the modulus $10^k$ variable and therefore, receive a solution dependent on $k\;$?

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?

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 dependent on k?