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On The Ternary Quadratic Diophantine Equation

ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538

Volume 11 Issue III Mar 2023- Available at www.ijraset.com

Equation (15) is written in the form of a ratio as

This is equivalent to the following two equations

By using cross-multiplication, we get

Replacing the preceding variables of and  in equation (2), the equivalent integer answers to (1) are provided by

IV. CONCLUSION

In this paper, We have found an endless number of non-zero distinct integer solutions to the ternary quadratic Diophantine equation

16 3 )

To sum up, one can look for other solution patterns and their accompanying attributes.

References

[1] Batta. B and Singh. A.N, History of Hindu Mathematics, Asia Publishing House 1938.

[2] Carmichael, R.D., “The Theory of Numbers and Diophantine Analysis”, Dover Publications,New York, 1959.

[3] Dickson. L.E., “History of the theory of numbers”, Chelsia Publishing Co., Vol.II, New York, 1952.

[4] G. Janaki and C. Saranya, Observations on the ternary quadratic Diophantine equation , International Journal of Innovative Research in Science, Engineering, and Technology 5(2) (2016), 2060-2065.

[5] G. Janaki and S. Vidhya, on the integer solutions of the homogeneous biquadratic Diophantine equation , International Journal of Engineering Science and Computing 6(6) (2016), 7275-7278.

[6] M. A. Gopalan and G. Janaki, Integral solutions of  

[7] G. Janaki and P. Saranya, on the ternary cubic Diophantine equation  

, Impact J. Sci. Tech. 4(1) (2010), 97-102.

, International Journal of Science and Research-online 5(3) (2016), 227-229.

[8] G. Janaki and C. Saranya, Integral solutions of the ternary cubic equation , International Research Journal of Engineering and Technology 4(3) (2017), 665-669.