Is f(x) Holomorphic if f(x)^2 and f(x)^3 Are?

[iamqsqsqs]

If we know f(x)^2 and f(x)^3 are both holomorphic, can we say that f(x) itself is also holomorphic? And how to prove that?

 

[mathwonk]

have you tried dividing them?

 

[iamqsqsqs]

just figure out how to do it. just divide them and prove that the singularities must be isolated. otherwise f(z) will be constantly 0.

 

[lavinia]

If we know f(x)^2 and f(x)^3 are both holomorphic, can we say that f(x) itself is also holomorphic? And how to prove that?

prove that the derivatives of a holomorphic function are holomorphic