MathDB

Let

f : \mathbb{N} \mapsto \mathbb{N}

be such that (i)

f

is strictly increasing; (ii) f(mn) \equal{} f(m)f(n) \forall m, n \in \mathbb{N}; and (iii) if

m \neq n

and m^n \equal{} n^m, then f(m) \equal{} n or f(n) \equal{} m. Determine

f(30).

96