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Can you find two non-constant meromorphic functions $f,g$ such that $f^3 +g^3=1$?

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    If there is one pair, then the identity, $$\left(\frac{x^3y + y}{x y^3 + x}\right)^3+\left(\frac{x^3 - y^3}{x y^3 + x}\right)^3=1,\quad \text{if}\; x^3+y^3=1$$ should lead to many more parametrizations.2017-01-09

3 Answers 3