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arXiv · 1705.05044

Diophantine equations in separated variables and lacunary polynomials

Dijana Kreso
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Abstract

We study Diophantine equations of type $f(x)=g(y)$, where $f$ and $g$ are lacunary polynomials. According to a well known finiteness criterion, for a number field $K$ and nonconstant $f, g\in K[x]$, the equation $f(x)=g(y)$ has infinitely many solutions in $S$-integers $x, y$ only if $f$ and $g$ are representable as a functional composition of lower degree polynomials in a certain prescribed way. The behaviour of lacunary polynomials with respect to functional composition is a topic of independent interest, and has been studied by several authors. In this paper we utilize known results and develop some new results on the latter topic.

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Dijana Kreso. 2017-05-15. Diophantine equations in separated variables and lacunary polynomials. https://arxiv.org/abs/1705.05044

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