IMO 1989 LL THA98

Let f : N oN be such that

imolonglistmathematicsolympiad

IMO 1989 LL THA98

Origin: THA

Problem

Let f : N \toN be such that (i) f is strictly increasing; (ii) f(mn) = f(m)f(n) \forallm, n \inN; and (iii) if m ̸= n and mn = nm, then f(m) = n or f(n) = m. Determine f(30).