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Observations on the Binary Quadratic Diophantine Equation x2 - 2xy -y2 + 2x +14y= 72

G. Janaki1 , C. Saranya2

  1. Department of Mathematics, Cauvery College for Women, Trichy-18, India.
  2. Department of Mathematics, Cauvery College for Women, Trichy-18, India.

Correspondence should be addressed to: c.saranyavinoth@gmail.com.


Section:Review Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.152-155, Apr-2020


Online published on Apr 30, 2020


Copyright © G. Janaki , C. Saranya . 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: G. Janaki , C. Saranya, “Observations on the Binary Quadratic Diophantine Equation x2 - 2xy -y2 + 2x +14y= 72,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.2, pp.152-155, 2020.

MLA Style Citation: G. Janaki , C. Saranya "Observations on the Binary Quadratic Diophantine Equation x2 - 2xy -y2 + 2x +14y= 72." International Journal of Scientific Research in Mathematical and Statistical Sciences 7.2 (2020): 152-155.

APA Style Citation: G. Janaki , C. Saranya, (2020). Observations on the Binary Quadratic Diophantine Equation x2 - 2xy -y2 + 2x +14y= 72. International Journal of Scientific Research in Mathematical and Statistical Sciences, 7(2), 152-155.

BibTex Style Citation:
@article{Janaki_2020,
author = {G. Janaki , C. Saranya},
title = {Observations on the Binary Quadratic Diophantine Equation x2 - 2xy -y2 + 2x +14y= 72},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {4 2020},
volume = {7},
Issue = {2},
month = {4},
year = {2020},
issn = {2347-2693},
pages = {152-155},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1845},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1845
TI - Observations on the Binary Quadratic Diophantine Equation x2 - 2xy -y2 + 2x +14y= 72
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - G. Janaki , C. Saranya
PY - 2020
DA - 2020/04/30
PB - IJCSE, Indore, INDIA
SP - 152-155
IS - 2
VL - 7
SN - 2347-2693
ER -

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Abstract :
The binary quadratic equation represents a hyperbola is analyzed for its non-zero distinct integer solutions. In this paper, we obtain a sequence of its integral solutions and present a few interesting relations among them.

Key-Words / Index Term :
Binary quadratic equation, Integral solutions, Hyperbola, Parabola & Pell’s equation.

References :
[1] Banumathy.T.S., (1995) A Modern Introduction to Ancient Indian Mathematics, Wiley Eastern Limited, London.
[2] Carmichael, R.D., (1950) The Theory of Numbers and Diophantine Analysis, Dover Publications, NewYork.
[3] Dickson. L. E., (1952) History of The Theory of Numbers, Vol.II, Chelsia Publicating Co, New York.
[4] Gopalan,M.A., and Parvathy,G., (2010) “Integral Points On The Hyperbola x2 + 4xy + y2 - 2x -10 y + 24 = 0,”Antarctica J.Math,Vol 1(2),149-155.
[5] Gopalan,M.A, Vidhyalakshmi,S, Sumathi.G and Lakshmi.K, Sep (2010) “”Integral Points On The Hyperbola x 2 + 6xy + y 2 + 40x + 8 y + 40 = 0 ” , Bessel J.Math. Vol 2(3),159-164.
[6] Gopalan,M.A., Gokila,K.,and Vidhyalakshmi,S., (2007), “On the Diophantine Equation x 2 + 4xy + y 2 - 2x + 2 y - 6 = 0”, Acta Ciencia Indica, Vol.XXXIIIM No.2, pp. 567-570.
[7] Gopalan,M.A.,Vidhyalakshmi,S.,and Devibala,S., (2007), On The Diophantine Equation 3x2+ xy = 14, Acta Ciencia Indica, Vol.XXXIII M.No.2, pp.645-646.
[8]Gopalan.M.A., and Janaki.G., (2008), “Observations on x 2 - y 2 + x + y + xy = 2”, Impact J.Sci.,Tech, Vol.2(3), pp.143-148.
[9]Gopalan.M.A., Shanmuganadham,P., and Vijayashankar,A., (2008), “On Binary Quadratic Equation x 2 - 5xy + y 2 + 8x - 20 y + 15 = 0 ”, Acta Ciencia Indica,Vol . XXXIVM. No.4, pp.1803-1805.
[10]Gopalan,M.A, Vidhyalakahmi,S, Lakshmi.K and Sumathi.G, (2012) “ Observation on 3x2 +10xy + 4 y2 - 4x + 2 y - 7 = 0 ” , Diophantus J.Maths.Vol.1(2),123-125.
[11] Vidhyalakshmi,S, Gopalan,M.A and Lakshmi.K, (2014) “ Observation On The Binary Quadratic Equation 3x2 - 8xy + 3y2 + 2x + 2 y + 6 = 0”, Scholar Journal of Physics, Mathematics and Statistics, Vol.1(2), (Sep-Nov), 41-45.
[12] Vidhyalakshmi. S, Gopalan,M.A and Lakshmi.K, August( 2014) “Integer Solution of the Binary Quadratic Equation x2 - 5xy + y2 + 33x = 0”, International Journal of Innovative Science Engineering &Technology, Vol.1(6), 450-453.

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