We look for non–trivial integer solution to the equation for the singular choices of particular by (i) t = 2k (ii) t = 2k+1, Additionally, recurrence relations on the solutions are obtained.
Introduction
Conclusion
In this paper, we have presented infinitely many integer solutions for the represented by the negative Pell equation As the binary quadratic Diophantine equations are rich in variety, one may search for the other choices of negative Pell equations and determine their integer solutions along with suitable properties.
References
[1] Carmichael R.D, History of Theory of numbers and Diophantine Analysis, Dover Publication, New York, 1959.
[2] Nagell T, Introduction to Number Theory, Chelsea publishing company, New York, 1982.
[3] Mordell L.J, Diophantine equations, Academic press, London, 1969.
[4] Janaki G, Vidhya S (2016), On the integer solutions of the Pell equation ,International Journal Of Scientific Research in Science, Engineering and Technology,2(2),1195-1197.
[5] Janaki G, Vidhya S (2016), On the integer solutions of the Pell equation International Journal Multidisciplinary Research and Development,3(5), 39-42.
[6] Janaki G, Vidhya S (2016), On the negative Pell equation , International Journal Of Applied Research,2(11),462-466.
[7] Vidhya S, Janaki G (2017), Observation on , International Journal Of Statistics and Applied Mathematics, 2(3), 04-05.
[8] Vidhya S, Janaki G (2018)An integral solution of negative Pell’s equation involving two-digit sphenic numbers, International Journal Of Computer Sciences and Engineering, 6,444-445.
[9] Vidhya S, Janaki G (2019), Observation on Remarkable Diophantine Equation, Compliance Engineering Journal, 10(12), 667-670.
[10] Vidhya S, Janaki G (2019), Observation on , International Journal for science and Advance Research in Technology, 5(12), 232-233.
[11] Janaki, G., & Vidhya, S. (2016). Rectangle with area as a special polygonal number. International Journal of Engineering Research, 4, 88-91.
[12] Janaki, G., & Vidhya, S. Special pairs of rectangles and Sphenic number. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 4, 376-378.