On the problem of Pillai with Padovan numbers and powers of 3

Mahadi Ddamulira

doi:10.1556/012.2019.56.3.1435

On the problem of Pillai with Padovan numbers and powers of 3

Mahadi Ddamulira

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

Let $\{P_n\_{n \ge 0}$ be the sequence of Padovan numbers defined by $P_0 = 0, P_1 = 1, P_2 = 1$, and $P_{n+3} = P_{n+1} + P_n$ for all $n \ge 0$. In this paper, we find all integers $c$ admitting at least two representations as a difference between a Padovan number and a power of $3$.

Original language	English
Pages (from-to)	364–379
Journal	Studia Scientiarum Mathematicarum Hungarica
Volume	56
Issue number	3
DOIs	https://doi.org/10.1556/012.2019.56.3.1435
Publication status	Published - 13 Oct 2019

Keywords

Padovan number
Linear forms in logarithms
Baker's method

ASJC Scopus subject areas

Algebra and Number Theory

Fields of Expertise

Information, Communication & Computing

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10.1556/012.2019.56.3.1435

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abstract = "Let $\{P_n\_{n \ge 0}$ be the sequence of Padovan numbers defined by $P_0 = 0, P_1 = 1, P_2 = 1$, and $P_{n+3} = P_{n+1} + P_n$ for all $n \ge 0$. In this paper, we find all integers $c$ admitting at least two representations as a difference between a Padovan number and a power of $3$.",

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KW - Padovan number

KW - Linear forms in logarithms

KW - Baker's method

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DO - 10.1556/012.2019.56.3.1435

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ER -

On the problem of Pillai with Padovan numbers and powers of 3

Abstract

Keywords

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