The Diophantine equation 𝛼₁^{𝑥₁}⋯𝛼_{𝑛}^{𝑥_{𝑛}}=𝑓(𝑥₁,…,𝑥_{𝑛}). II

Corvaja, P.; Schmidt, W.; Zannier, U.

doi:10.1090/S0002-9947-09-05012-0

The Diophantine equation $\alpha _{1}^{x_{1}}\cdots \alpha _{n}^{x_{n}} = f(x_{1},\dots ,x_{n})$. II
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by P. Corvaja, W. M. Schmidt and U. Zannier PDF

Trans. Amer. Math. Soc. 362 (2010), 2115-2123 Request permission

Abstract:

We will deal with the equation of the title where $\alpha _{1},\dots ,\alpha _{n}$ are multiplicatively independent complex numbers and $f$ is a polynomial. We will give a bound for the number of solutions which depends only on $n$ and the degree of $f$. Two further results which play a rôle in the proof are of independent interest.

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