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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
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