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Some Non-Extendable Diophantine Triples Involving Centered Square Numbers

C. Saranya1 , G. Janaki2

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.6 , pp.105-107, Dec-2019


Online published on Dec 31, 2019


Copyright © C. Saranya, G. Janaki . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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IEEE Style Citation: C. Saranya, G. Janaki, “Some Non-Extendable Diophantine Triples Involving Centered Square Numbers,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.6, pp.105-107, 2019.

MLA Style Citation: C. Saranya, G. Janaki "Some Non-Extendable Diophantine Triples Involving Centered Square Numbers." International Journal of Scientific Research in Mathematical and Statistical Sciences 6.6 (2019): 105-107.

APA Style Citation: C. Saranya, G. Janaki, (2019). Some Non-Extendable Diophantine Triples Involving Centered Square Numbers. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(6), 105-107.

BibTex Style Citation:
@article{Saranya_2019,
author = {C. Saranya, G. Janaki},
title = {Some Non-Extendable Diophantine Triples Involving Centered Square Numbers},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {12 2019},
volume = {6},
Issue = {6},
month = {12},
year = {2019},
issn = {2347-2693},
pages = {105-107},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1633},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1633
TI - Some Non-Extendable Diophantine Triples Involving Centered Square Numbers
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - C. Saranya, G. Janaki
PY - 2019
DA - 2019/12/31
PB - IJCSE, Indore, INDIA
SP - 105-107
IS - 6
VL - 6
SN - 2347-2693
ER -

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Abstract :
In this paper, we accomplish three non-extendable Diophantine triples of the form {a, b, 2(a+b-Square of the difference of the ranks)} involving centered square numbers with property D(-Square of the difference of the ranks).

Key-Words / Index Term :
Diophantine Triples, Centered Square Number, Non-extendability

References :
[1] Carmichael, R.D. “History of Theory of numbers and Diophantine Analysis”, Dover Publication, Newyork, 1959
[2] Mordell, L.J. “Diophantine equations”, Academic press, London, 1969
[3] Nagell, T. “Introduction to Number theory”, Chelsea publishing company, Newyork, 1981
[4] Hua, L.K. “Introduction to the Theory of Numbers”, Springer-Verlag, Berlin-Newyork, 1982
[5] Oistein Ore, “Number theory and its History”, Dover publications, Newyork, 1988
[6] Fujita, Y. “The extendability of Diphantine pairs ”, Journal of Number Theory, 128, 322-353, 2008
[7] Gopalan, M.A. and Pandichelvi, V., “On the extendability of the Diophantine triple involving Jacobsthal numbers ”, International Journal of Mathematics & Applications, 2(1), 1-3, 2009
[8] Janaki, G. and Saranya, C., “Special Dio 3-tuples for pentatope number”, Journal of Mathematics and Informatics, vol.11, Special issue, 119-123, 2017
[9] Janaki, G. and Saranya, C., “Construction of the Diophantine Triple involving Pentatope Number”, International Journal for Research in Applied Science & Engineering Technology, vol.6, issue III, 2317-2319, 2018
[10] Saranya, C. and G.Janaki, G., “Integer triples comprising of Jarasandha numbers in Arithmetic progression & Geometric progression”, International Journal of Research and Analytical Reviews, vol.6, issue 1, 751-752, 2019
[11] Gopalan, M.A, Vidhyalakshmi, S. and Thiruniraiselvi, N., “Some non-extendable diophantine triples in special number patterns”, International Journal of Innovative research and Review, Vol. 2 (3), pp.1-7, 2014

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