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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 5 | Year 2019 | Article Id. IJMTT-V65I5P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I5P505

On The Negative Pell Equation Y2 = 30x2 - 45


D. Maheswari, A.Mercy Carolin
Abstract

The binary quadratic Diophantine equation represented by the negative pellian is analyzed for its non-zero distinct solutions. A few interesting relations among the solutions are given. Further, employing the solutions of the above hyperbola, we have obtained solutions of other choices of hyperbolas, parabolas.

Keywords
Binary quadratic, Hyperbola, Parabola, Integral solutions, Pell equation.
References

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[2] L.J.Mordel, Diophantine equations, Academic Press, New York, 1969.
[3] S.J.Telang, Number Theory, Tata McGraw Hill Publishing company Limited, New Delhi,2000.
[4] D.M.Burton, Elementary Number Theory, Tata McGraw Hill Publishing company Limited, New Delhi, 2002.
[5] M.A.Gopalan,S.Vidhyalakshmi and D.Maheswari, “Observations on the hyperbola y2=30x2+1, IJOER, Vol-1, Issue 3,312- 314, 2013,.
[6] M.A.Gopalan, S.Vidhyalakshmi and A.Kavitha, Observations on the Hyperbola 10y2-3x2 = 13 , Archimedes J.Math.,3(1), 31-34, 2013.
[7] R.Suganya,D.Maheswari, “ On the negative pellian equation y2=110x2-29",Journal of mathematics and informatics, Vol-11,63-71,2017.
[8] S.Vidhyalakshmi, A.Kavitha and M.A.Gopalan, Observations on the Hyperbola ax2-(a+1)y2 =3a-1 , Discovery, 4(10), 22-24, 2013.
[9] M.A.Gopalan, S.Vidhyalakshmi and D.Maheswari, Observations on the Hyperbola y2=34x2+1,Bulletin of mathematics and statistics research, Vol-2, Issue 4, 414-417,2014.
[10] S.Vidhyalakshmi, A.Kavitha and M.A.Gopalan, Integral points on the Hyperbola x2-4xy+y2+15x=0 , Diophantus J.Maths,1(7), 338-340, 2014.

Citation :

D. Maheswari, A.Mercy Carolin, "On The Negative Pell Equation Y2 = 30x2 - 45," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 5, pp. 32-40, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I5P505

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