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Journals / Journal of Advanced Mathematics and Mathematics Education / 2023 / Cilt: 6 Sayı: 2

Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs

Özen ÖZER
Pages
1–7
Publication Date
2023-05-17
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Lastly, it is proved that {2, s, a_s} can not be extended Diophantine P_2 quadruples using elementary and algebraic methods different from other works in the literaure.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Although it is known that there are an infinite number of Diophantine P_1 triples, there is no complete characterization for these triples.
📊
Key Findings & Data:This paper is a continuation and a generalization of one of the recent papers (see [ ref. 35 ]) in which several numerical results are demonstrated and some properties are given for special Diophantine P_2 pairs and triples.
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Conclusion & Impact:Lastly, it is proved that {2, s, a_s} can not be extended Diophantine P_2 quadruples using elementary and algebraic methods different from other works in the literaure.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Diophantine P_2 sets · System of Equations · Integral Solutions

Abstract

Although it is known that there are an infinite number of Diophantine P_1 triples, there is no complete characterization for these triples. This paper is a continuation and a generalization of one of the recent papers (see [ ref. 35 ]) in which several numerical results are demonstrated and some properties are given for special Diophantine P_2 pairs and triples. Here, the expansion of the single-element set {2} into a Diophantine P_2 binary special family as {2, s} (with s values expressed as a recurrence/iteration of natural numbers) is obtained firstly. Then, binary special family {2, s} is extended as {2, s, a_s} Diophantine P_2 triples ( a_s is determined in the terms of s ) using solutions of Diophantine equations. Lastly, it is proved that {2, s, a_s} can not be extended Diophantine P_2 quadruples using elementary and algebraic methods different from other works in the literaure.

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Cite This Article

ÖZER, Ö. (2023). Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs. Journal of Advanced Mathematics and Mathematics Education, Cilt: 6 Sayı: 2, 1–7. https://ajindex.com/articles/937752

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References (1)

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