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arXiv · 2008.10342

Diophantine equations in separated variables and polynomial power sums

Clemens Fuchs·Sebastian Heintze
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Abstract

We consider Diophantine equations of the shape $ f(x) = g(y) $, where the polynomials $ f $ and $ g $ are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions $ (x,y) $ with a bounded denominator are only possible in trivial cases.

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Clemens Fuchs, Sebastian Heintze. 2020-08-24. Diophantine equations in separated variables and polynomial power sums. https://doi.org/10.1007/s00605-021-01560-6

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