Meromorphic functions sharing three values (Q5917526)

Let \(f\) and \(g\) be two meromorphic functions sharing three values counting multiplicities. Suppose that \(N_{1}(r, 1/(f-a))\neq T(r,f)+S(r,f)\) for some further value \(a,\) where \(N_{1}(r,\cdot)\) counts simple poles. It is shown that then \(f\) and \(g\) take one of six explicitly given particular forms.