nmmnthrowaway

10 ms·

1. 1.▲
   by nmmnthrowaway 3y ago

   Yes, but there is a much simpler proof.
2. 2.▲
   by nmmnthrowaway 3y ago

   That is correct. Why are there no others?
3. 3.▲
   by nmmnthrowaway 3y ago

   I think a more interesting problem to consider after solving n^m = m^n is solving n^m = m^n + 1 in the natural numbers.
4. 4.▲
   by nmmnthrowaway 3y ago

   n^n * n^(m - n) = n ^ m = m ^ n, so n^n divides m^n, so n divides m.