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arXiv · 2207.12868

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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Abstract

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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Herbert Batte, Mahadi Ddamulira, Juma Kasozi, Florian Luca. 2022-07-24. On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime. https://arxiv.org/abs/2207.12868

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