Ijraset Journal For Research in Applied Science and Engineering Technology

Abstract

The homogenous biquadratic Diophantine equation with five unknowns non-zero unique integer solutions are found using several techniques. The unusual numbers and the solutions are found to have a few intriguing relationships. The relationships between the solutions’ recurrences are also shown.

Introduction

Conclusion

Other non-zero unique integer solutions to the multivariable biquadratic equations under consideration may be sought after.

References

[1] Carmicheal R.D, The Theory of Numbers and Diophantine Analysis, Dover Publications, New York, 1959. [2] Dickson.L.E., “History of the Theory of Numbers”, Chelsea Publishing Company, New York. Vol II. 1952. [3] Mordell. L.J, “Diophantine equations”, Academic Press, New York, 1969. [4] Telang. S.G., “Number Theory”, Tata McGraw-Hill Publishing Company Limited, New Delhi,1996 [5] Nigel D. Smart, The Algorithmic Resolutions of Diophantine Equations, Cambridge University Press, London, 1999. [6] Gopalan M.A and Janaki G, Integral solutions of the ternary quartic equation , Impact J.Sci. Tech, Vol 2, issue 2, 71-79, 2008. [7] Gopalan M.A and Kalingarani J, Quartic equation in five unknowns , Bulletin of pure and applied sciences, Volume 28, issue 2, 305-311, 2009. [8] Gopalan M.A and Kalingarani J, Quartic equation in five unknowns , Bessel J. Math, Vol 1, issue 1, 49-57, 2011. [9] Gopalan M.A and Shanmuganandham P, On the biquadratic equation , Impact J.Sci. Tech, Vol 4, issue 4,111-115, 2010. [10] Gopalan M.A and Shanmuganandham P, On the Biquadratic equation , Bessel J. Math, vol 2, Issue 2, 87-91, 2012.

Copyright

Copyright © 2023 G Janaki, M. Krishnaveni. 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.