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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=k$, where $k\in\{\pm1,\pm4\}$, which is a Padovan number, with a few exceptions that we completely characterize.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=k$, where $k\in\{\pm1,\pm4\}$, which is a Padovan number, with a few exceptions that we completely characterize.
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Key Findings & Data:In this paper, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=k$, where $k\in\{\pm1,\pm4\}$, which is a Padovan number, with a few exceptions that we completely characterize.
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Conclusion & Impact:In this paper, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=k$, where $k\in\{\pm1,\pm4\}$, which is a Padovan number, with a few exceptions that we completely characterize.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Padovan numbers · Pell equation · Linear form in logarithms
Abstract
In this paper, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=k$, where $k\in\{\pm1,\pm4\}$, which is a Padovan number, with a few exceptions that we completely characterize.
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Cite This Article
RIHANE, S. E., HERNANE, M. O., TOGBE, A. (2019). The $X$-coordinates of Pell equations and Padovan numbers. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 207–223. https://ajindex.com/articles/214997