Herbert Batte, Mahadi Ddamulira, Juma Kasozi, F. Luca
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On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime
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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