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

Herbert Batte, Mahadi Ddamulira, Juma Kasozi, Florian Luca

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Source: Crossref

Published: Dec 30, 2022

DOI: 10.3336/gm.57.2.02

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Source 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 $m_{F,p}(c)\le 4$ .

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