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Construction of Diophantine Triples Involving Hexagonal Pyramidal Numbers

C. Saranya1 , K. Manjula2

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.4 , pp.41-43, Aug-2022


Online published on Aug 31, 2022


Copyright © C. Saranya, K. Manjula . 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, K. Manjula, “Construction of Diophantine Triples Involving Hexagonal Pyramidal Numbers,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.4, pp.41-43, 2022.

MLA Style Citation: C. Saranya, K. Manjula "Construction of Diophantine Triples Involving Hexagonal Pyramidal Numbers." International Journal of Scientific Research in Mathematical and Statistical Sciences 9.4 (2022): 41-43.

APA Style Citation: C. Saranya, K. Manjula, (2022). Construction of Diophantine Triples Involving Hexagonal Pyramidal Numbers. International Journal of Scientific Research in Mathematical and Statistical Sciences, 9(4), 41-43.

BibTex Style Citation:
@article{Saranya_2022,
author = {C. Saranya, K. Manjula},
title = {Construction of Diophantine Triples Involving Hexagonal Pyramidal Numbers},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {8 2022},
volume = {9},
Issue = {4},
month = {8},
year = {2022},
issn = {2347-2693},
pages = {41-43},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=2902},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=2902
TI - Construction of Diophantine Triples Involving Hexagonal Pyramidal Numbers
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - C. Saranya, K. Manjula
PY - 2022
DA - 2022/08/31
PB - IJCSE, Indore, INDIA
SP - 41-43
IS - 4
VL - 9
SN - 2347-2693
ER -

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Abstract :
We scrutinize for three particular polynomials with integer coefficients to such an extent that the result of any two numbers expanded by a non-zero number (or polynomials with number coefficients) is a perfect square.

Key-Words / Index Term :
Dio triples, pyramidal numbers, Hexagonal pyramidal number, polynomials, integers, perfect square.

References :
[1] Beardon, A.F. and Deshpande, M.N., “Diophantine triples”, The Mathematical Gazette, vol.86. pp. 258-260, 2002.
[2] Bugeaud, Y.Dujella, A. and Mignotte, M., “On the family of Diophantine triples” {K-1, K+1, 16K3-4K}, Glasgow Math. J. vol.49. pp. 333-344, 2007.
[3] Carmichael, R.D. “Theory of numbers and Diophantine triples”, Dover Publications.
[4] Deshpande, M.N. “Families of Diophantine triples”, Bulletin of the Marathwada Mathematical Society, vol 4. pp. 19-21, 2003.
[5] Hua, L.K. “Introduction to the Theory of Numbers”, Springer-Verlag, Berlin-New York, 1982.
[6] 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, March 2018.
[7] Janaki, G. and Saranya, C. “Special Dio 3-tuples for pentatope number”, Journal of Mathematics and Informatics, vol.11, Special issue, 119-123, Dec 2017.
[8] Janaki, G. and Saranya, C., “Half companion sequences of special dio 3-tuples involving centered square numbers”, International Journal for Recent Technology and Engineering, vol.8, issue 3, 3843-3845, September 2019.
[9] Saranya C., and Janaki G., “Some Non-extendable Diophantine Triples involving centered square numbers”, International Journal of Scientific Research in Mathematical and Statistical Sciences, vol 6, Issue 6, 105-107, December 2019.
[10] Saranya C., and Achya. B., “Special Diophantine triples involving square pyramidal numbers”, Indian Journal of Advanced Mathematics, Volume 1, Issue 2, 27-29, October 2021.
[11] Saranya C., and Mahalakshmi, E., “Dio-Triples involving pentagonal pyramidal numbers”, International Journal of Scientific Research in Mathematical and Statistical Sciences, vol 8, Issue 6, 45-48, December 2021.
[12] Saranya C., and Achya. B., “Diophantine triples involving square pyramidal numbers”, Advances and Applications in Mathematical Sciences, Volume 21, Issue 3, 1541-1547, January 2022.

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