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Entire functions that share one value. (English) Zbl 0899.30022
The authors prove: Let $$f$$ and $$g$$ be nonconstant entire functions, $$n> 6$$, $$\psi= {f^{(n)} f'-1 \over g^{(n)} g'-1}$$. If $$\psi$$ and $${1\over\psi}$$ are entire functions then $$f^{(n)} f'g^{(n)} g'=1$$ or $$f=tg$$ with $$t^{n+1} =1$$.

MSC:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory