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

Özen Özer

EN

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

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.

Keywords

Diophantine P_2 sets, System of Equations, Integral Solutions, Non- extendable Diophantine P_2 triples, Elementary Number Theory, Natural Numbers.

Supporting Institution

Kırklareli Üniversitesi BAPKO

Project Number

KLUBAP-233

Thanks

The study is supported by Scientific Research Project with number KLUBAP-233 of Kırklareli University.

References

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Details

Primary Language

English

Subjects

Mathematical Sciences, Applied Mathematics

Journal Section

Research Article

Authors

Özen Özer ^*
0000-0001-6476-0664
Türkiye

Publication Date

May 17, 2023

Submission Date

February 10, 2023

Acceptance Date

March 10, 2023

Published in Issue

Year 2023 Volume: 6 Number: 2

IZ

https://izlik.org/JA73LR35GS

APA

Özer, Ö. (2023). Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs. Journal of Advanced Mathematics and Mathematics Education, 6(2), 1-7. https://izlik.org/JA73LR35GS

AMA

1.Özer Ö. Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs. JAMAME. 2023;6(2):1-7. https://izlik.org/JA73LR35GS

Chicago

Özer, Özen. 2023. “Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs”. Journal of Advanced Mathematics and Mathematics Education 6 (2): 1-7. https://izlik.org/JA73LR35GS.

EndNote

Özer Ö (May 1, 2023) Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs. Journal of Advanced Mathematics and Mathematics Education 6 2 1–7.

IEEE

[1]Ö. Özer, “Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs”, JAMAME, vol. 6, no. 2, pp. 1–7, May 2023, [Online]. Available: https://izlik.org/JA73LR35GS

ISNAD

Özer, Özen. “Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs”. Journal of Advanced Mathematics and Mathematics Education 6/2 (May 1, 2023): 1-7. https://izlik.org/JA73LR35GS.

JAMA

1.Özer Ö. Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs. JAMAME. 2023;6:1–7.

MLA

Özer, Özen. “Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs”. Journal of Advanced Mathematics and Mathematics Education, vol. 6, no. 2, May 2023, pp. 1-7, https://izlik.org/JA73LR35GS.

Vancouver

1.Özen Özer. Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs. JAMAME [Internet]. 2023 May 1;6(2):1-7. Available from: https://izlik.org/JA73LR35GS

Baş editör; Prof .Dr. Seyfullah Hızarcı

Abstract

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

Abstract

Keywords

Supporting Institution

Project Number

Thanks

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

IZ

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