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Abstract
In this paper, we consider a variant of Pillai's problem over function fields F in one variable over C. For given simple linear recurrence sequences G _{n} and H _{m}, defined over F and satisfying some weak conditions, we will prove that the equation G _{n}−H _{m}=f has only finitely many solutions (n,m)∈N ^{2} for any nonzero f∈F, which can be effectively bounded. Furthermore, we prove that under suitable assumptions there are only finitely many effectively computable f with more than one representation of the form G _{n}−H _{m}.
Original language  English 

Pages (fromto)  278292 
Number of pages  15 
Journal  Journal of Number Theory 
Volume  222 
DOIs  
Publication status  Published  May 2021 
Fields of Science and Technology Classification 2012
 101 Mathematics
Keywords
 Diophantine equations
 Linear recurrences
 Pillai's problem
Projects
 1 Active

Diophantine number theory
Fuchs, C., Tichy, R., Györy, K. & Hajdu, L.
1/04/20 → 31/03/24
Project: Research