# A function field variant of Pillai's problem

@article{Fuchs2020AFF,
title={A function field variant of Pillai's problem},
author={Clemens Fuchs and Sebastian Heintze},
journal={arXiv: Number Theory},
year={2020}
}
• Published 24 August 2020
• Mathematics
• arXiv: Number Theory
3 Citations
Pillai's conjecture for polynomials
In this paper we study the polynomial version of Pillai’s conjecture on the exponential Diophantine equation p − q = f. We prove that for any non-constant polynomial f there are only finitely many
$S$-unit values of $G_n + G_m$ in function fields
In this paper we consider a simple linear recurrence sequence Gn defined over a function field in one variable over the field of complex numbers. We prove an upper bound on the indices n and m such
Asymptotics for Pillai's problem with polynomials
Let a1(x)p1(x)+ · · ·+ak(x)pk(x) n as well as b1(x)q1(x)+ · · ·+ bl(x)ql(x) m be two polynomial power sums where the complex polynomials pi(x) and qj(x) are all non-constant. Then in the present

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In this paper, we establish a number of theorems on the classic Diophantine equation of S. S. Pillai, a x − b y = c ,w herea, b and c are given nonzero integers with a,b ≥ 2. In particular, we obtain
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