In [7], R. Nevanlinna gave the following uniqueness theorem of meromorphic functions as an improvement of a result of G. Pólya ([8]).
Theorem A. Let f, g be non-constant meromorphic functions on C. If there are five mutually distinct values a1, …, a5 such that f−1(ai = g−1(ai) (1 ≦ i ≦ 5), then f ≡ g.