Rational functions with linear relations

Masuda, Ariane; Zieve, Michael

doi:10.1090/S0002-9939-07-09246-5

Rational functions with linear relations
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by Ariane M. Masuda and Michael E. Zieve PDF

Proc. Amer. Math. Soc. 136 (2008), 1403-1408 Request permission

Abstract:

We find all polynomials $f,g,h$ over a field $K$ such that $g$ and $h$ are linear and $f(g(x))=h(f(x))$. We also solve the same problem for rational functions $f,g,h$, in case the field $K$ is algebraically closed.

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