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

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

doi:10.3336/gm.57.2.02

Glasnik matematički, Vol. 57 No. 2, 2022.

Original scientific paper

https://doi.org/10.3336/gm.57.2.02

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

Herbert Batte orcid.org/0000-0003-3882-0189 ; Department of Mathematics, Makerere University, Kampala, Uganda
Mahadi Ddamulira orcid.org/0000-0002-4273-0066 ; Department of Mathematics, Makerere University, Kampala, Uganda
Juma Kasozi ; Department of Mathematics, Makerere University, Kampala, Uganda
Florian Luca orcid.org/0000-0003-1321-4422 ; School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa

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APA 6th Edition

Batte, H., Ddamulira, M., Kasozi, J. & Luca, F. (2022). On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime. Glasnik matematički, 57 (2), 185-201. https://doi.org/10.3336/gm.57.2.02

MLA 8th Edition

Batte, Herbert, et al. "On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime." Glasnik matematički, vol. 57, no. 2, 2022, pp. 185-201. https://doi.org/10.3336/gm.57.2.02. Accessed 22 Dec. 2024.

Chicago 17th Edition

Batte, Herbert, Mahadi Ddamulira, Juma Kasozi and Florian Luca. "On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime." Glasnik matematički 57, no. 2 (2022): 185-201. https://doi.org/10.3336/gm.57.2.02

Harvard

Batte, H., et al. (2022). 'On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime', Glasnik matematički, 57(2), pp. 185-201. https://doi.org/10.3336/gm.57.2.02

Vancouver

Batte H, Ddamulira M, Kasozi J, Luca F. On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime. Glasnik matematički [Internet]. 2022 [cited 2024 December 22];57(2):185-201. https://doi.org/10.3336/gm.57.2.02

IEEE

H. Batte, M. Ddamulira, J. Kasozi and F. Luca, "On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime", Glasnik matematički, vol.57, no. 2, pp. 185-201, 2022. [Online]. https://doi.org/10.3336/gm.57.2.02

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