On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime-Reference-Cited by-同舟云学术

On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime

Published:2022-12-30 Issue:2 Volume:57 Page:185-201
ISSN:0017-095X
Container-title:Glasnik Matematicki
language:
Short-container-title:Glas. Mat. Ser. III

Author:

Batte Herbert, ,Ddamulira Mahadi,Kasozi Juma,Luca Florian, , ,

Abstract

Let \( \{F_n\}_{n\geq 0} \) be the sequence of Fibonacci numbers and let \(p\) be a prime. For an integer \(c\) we write \(m_{F,p}(c)\) for the number of distinct representations of \(c\) as \(F_k-p^\ell\) with \(k\ge 2\) and \(\ell\ge 0\). We prove that \(m_{F,p}(c)\le 4\).

Publisher

University of Zagreb, Faculty of Science, Department of Mathematics

Subject

General Mathematics

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