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

Öz

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.

Anahtar Kelimeler

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

Destekleyen Kurum

Kırklareli Üniversitesi BAPKO

Proje Numarası

KLUBAP-233

Teşekkür

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

Kaynakça

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Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik, Uygulamalı Matematik

Bölüm

Araştırma Makalesi

Yazarlar

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

Yayımlanma Tarihi

17 Mayıs 2023

Gönderilme Tarihi

10 Şubat 2023

Kabul Tarihi

10 Mart 2023

Yayımlandığı Sayı

Yıl 2023 Cilt: 6 Sayı: 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. Journal of Advanced Mathematics and Mathematics Education. 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 (01 Mayıs 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”, Journal of Advanced Mathematics and Mathematics Education, c. 6, sy 2, ss. 1–7, May. 2023, [çevrimiçi]. Erişim adresi: 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 (01 Mayıs 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. Journal of Advanced Mathematics and Mathematics Education. 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, c. 6, sy 2, Mayıs 2023, ss. 1-7, https://izlik.org/JA73LR35GS.

Vancouver

1.Özen Özer. Some Notes on the Extendibility of an Especial Family of Diophantine P_2 Pairs. Journal of Advanced Mathematics and Mathematics Education [Internet]. 01 Mayıs 2023;6(2):1-7. Erişim adresi: https://izlik.org/JA73LR35GS

Öz

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

Öz

Anahtar Kelimeler

Destekleyen Kurum

Proje Numarası

Teşekkür

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

IZ

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