The Integer Solution of the Negative Pell Equation Involving Palindrome Numbers

Abstract

The objective of the article is to find an integer solution that is non-zero for the negative Pell’s equation involving Palindrome number Concerning the several possibilities for , , and The recurrence relation on the solutions is retrieved.

Introduction

Conclusion

This paper presents integer solutions to the negative Pell equation involving the palindrome number. Due to the Diophantine equation’s wide variety, one can look for other palindrome number to the Diophantine equations .

References

[1] Al – Zaid .H, Brindza .B and Printer .A, “On Positive integer solutions of the Equation ”, Canad.Math.Bull, Vol.39, pp.199, 1996 [2] An integral solution of negative Pell’s equation involving two-digit sphenic numbers, International Journal of Computer Sciences and Engineering, Vol.6, Issue.7, pp.444-445, 2018. [3] Bhanumurthy T.S, Ancient Indian Mathematics, New Age International Publishers Limited, New Delhi, 1995 [4] Borevich Z.I and Shafarevich I.R, Number Theory,Academic Press, New York, 1966 [5] Boyer C.B, “A History of Mathematics”, John Wiley & Sons Inc., New York, 1968 [6] Brown .E, “Diophantine equations of the form ”, J.ReineAngew.Math, Vol.274/275, pp.385-389, 1975 [7] Carmichael R.D, “Theory of Numbers and Diophantine Analysis”, Dover Publications Inc., New York, 1959 [8] Davenport Harold, “The Higher Arithmetic: An Introduction to the Theory of Numbers”, 7th Edition, Cambridge University Press, 1999. [9] Dudley .U, “Elementary Number Theory”, W.H. Freeman and Co., New York, 1969 [10] Gopalan M.A, Sangeetha .V and Manju Somanath, “On the integer solution of the Pell equation ”, International Journal of Applied Mathematical Research, Vol.3, No.1, pp.58-64, 2014 [11] G Janaki, S Vidhya Observation on , International Journal of Statistics and Applied Mathematics, Vol.2, Issue.3, pp.04-05, 2017 [12] Janaki.G, Vidhya.SOn the integer solutions of the Pell equation , International Journal of Multidisciplinary Research and Development, Vol.3, Issue.5, pp.39-42, 2016 [13] G.Janaki, S.VidhyaOn the integer solutions of the Pell equation ”, International Journal of Scientific Research in Science, Engineering and Technology, Vol.2, Issue.2, pp.1195-1197, 2016. [14] G.Janaki, S.VidhyaOn the negative Pell equation , International Journal of Applied Research, Vol.2, Issue.11, pp.462-466, 2016. [15] S,Vidhya, G.Janaki observation on ,International Journal for Science and Advance Research in Technology,vol.5,Issue.12,pp.232-233, 2019

Copyright

Copyright © 2024 S. Vidhya, V. Devi. 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.