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

Herbert Batte, Mahadi Ddamulira, Juma Kasozi and Florian Luca
arXiv.org
Cornell University Library, arXiv.org
24/07/2022

Abstract

Fibonacci numbers
Let \( \{F_n\}_{n\ge 0} \) 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 \(m_{F,p}(c)\le 4\).

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