Given $f$ defined at $G$ and $f^3,f^2$ holomorphic at G prove $f$ holomorphic
My try:
$f^3-f^2$=$f^2(f-1)$ because the LHS is holomorphic so does the RHS and then we get that $f-1$ is holomorphic and $f$ is holomorphic, is this right?
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Aryaman Maithani
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Omer Sonsino
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1This helps you directly only where $f\ne0$ – Hagen von Eitzen Jun 19 '20 at 12:37
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6Does this answer your question? Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic – it is demonstrated in the answers that the continuity condition is not needed. – Martin R Jun 19 '20 at 12:44
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Another one: https://math.stackexchange.com/q/2015016. – Martin R Jun 19 '20 at 12:52