nmmnthrowaway··on Tell HN: 2^4 == 4^2, extended to rationalsThat is correct. Why are there no others?
nmmnthrowaway··on Tell HN: 2^4 == 4^2, extended to rationalsI think a more interesting problem to consider after solving n^m = m^n is solving n^m = m^n + 1 in the natural numbers.
nmmnthrowaway··on Only one pair of distinct positive integers satisfy the equation m^n = n^mn^n * n^(m - n) = n ^ m = m ^ n, so n^n divides m^n, so n divides m.