Keywords:-
Keywords:
Quadratic Diophantine Equation, Polar Form, Euler’s Formula, Positive Integer Solutions.
Article Content:-
Abstract
Diophantine Equations named after ancient Greek mathematician Diophantus, plays a vital role not only in number theory but also in several branches of science. In this paper, we have solved an quadratic Diophantine equations where the right hand side are positive integral powers of 37 and provide its integer solutions. The method adopted to solve the given equation is using the concept of polar form of a particular complex number. This concept can be generalized for solving similar equations.
References:-
References
1. Andreescu, T., D. Andrica, and I. Cucurezeanu, An introduction to Diophantine equations: A problem-based approach, Birkhäuser Verlag, New York, 2010.
2. Andrews, G. E. 1971, Number theory, W. B. Saunders Co., Philadelphia, Pa.-London- Toronto, Ont.
3. R. Sivaraman, J. Suganthi, A. Dinesh Kumar, P.N. Vijayakumar, R. Sengothai, On Solving an Amusing Puzzle, Specialusis Ugdymas/Special Education, Vol 1, No. 43, 2022, 643 – 647.
4. R. Sivaraman, R. Sengothai, P.N. Vijayakumar, Novel Method of Solving Linear Diophantine Equation with Three Variables, Stochastic Modeling and Applications, Vol. 26, No. 3, Special Issue – Part 4, 2022, 284 – 286.
5. R. Sivaraman, On Solving Special Type of Linear Diophantine Equation, International Journal of Natural Sciences, Volume 12, Issue 70, 38217 – 38219, 2022.
6. R. Sivaraman, Summing Through Integrals, Science Technology and Development, Volume IX, Issue IV, April 2020, pp. 267 – 272.
7. R. Sivaraman, Bernoulli Polynomials and Ramanujan Summation, Proceedings of First International Conference on Mathematical Modeling and Computational Science, Advances in Intelligent Systems and Computing, Vol. 1292, Springer Nature, 2021, pp. 475 – 484.
8. R. Sengothai, R. Sivaraman, Solving Diophantine Equations using Bronze Ratio, Journal of Algebraic Statistics, Volume 13, No. 3, 2022, 812 – 814.
9. P.N.Vijayakumar, R. Sivaraman, On Solving Euler’s Quadratic Diophantine Equation, Journal of Algebraic Statistics, Volume 13, No. 3, 2022, 815 – 817.
10. A. Dinesh Kumar, R. Sivaraman, Asymptotic Behavior of Limiting Ratios of Generalized Recurrence Relations, Journal
11. P Senthil Kumar, R Abirami, A Dinesh Kumar, Fuzzy model for the effect of rhIL6 Infusion on Growth Hormone, International Conference on Advances in Applied Probability, Graph Theory and Fuzzy Mathematics, Vol. 252, 2014, pp. 246
12. P Senthil Kumar, A Dinesh Kumar, M Vasuki, Stochastic model to find the effect of gallbladder contraction result using uniform distribution, Arya Bhatta Journal of Mathematics and Informatics, Vol 6, No. 2, 2014, pp. 323 – 328
13. R. Sivaraman, Recognizing Ramanujan’s House Number Puzzle, German International Journal of Modern Science, 22, November 2021, pp. 25 – 27
14. R. Sivaraman, Pythagorean Triples and Generalized Recursive Sequences, Mathematical Sciences International Research Journal, Vol. 10, No. 2, July 2021, pp. 1 – 5
15. R. Sivaraman, Sum of powers of natural numbers, AUT AUT Research Journal, Volume XI, Issue IV, April 2020, pp. 353 – 359.
2. Andrews, G. E. 1971, Number theory, W. B. Saunders Co., Philadelphia, Pa.-London- Toronto, Ont.
3. R. Sivaraman, J. Suganthi, A. Dinesh Kumar, P.N. Vijayakumar, R. Sengothai, On Solving an Amusing Puzzle, Specialusis Ugdymas/Special Education, Vol 1, No. 43, 2022, 643 – 647.
4. R. Sivaraman, R. Sengothai, P.N. Vijayakumar, Novel Method of Solving Linear Diophantine Equation with Three Variables, Stochastic Modeling and Applications, Vol. 26, No. 3, Special Issue – Part 4, 2022, 284 – 286.
5. R. Sivaraman, On Solving Special Type of Linear Diophantine Equation, International Journal of Natural Sciences, Volume 12, Issue 70, 38217 – 38219, 2022.
6. R. Sivaraman, Summing Through Integrals, Science Technology and Development, Volume IX, Issue IV, April 2020, pp. 267 – 272.
7. R. Sivaraman, Bernoulli Polynomials and Ramanujan Summation, Proceedings of First International Conference on Mathematical Modeling and Computational Science, Advances in Intelligent Systems and Computing, Vol. 1292, Springer Nature, 2021, pp. 475 – 484.
8. R. Sengothai, R. Sivaraman, Solving Diophantine Equations using Bronze Ratio, Journal of Algebraic Statistics, Volume 13, No. 3, 2022, 812 – 814.
9. P.N.Vijayakumar, R. Sivaraman, On Solving Euler’s Quadratic Diophantine Equation, Journal of Algebraic Statistics, Volume 13, No. 3, 2022, 815 – 817.
10. A. Dinesh Kumar, R. Sivaraman, Asymptotic Behavior of Limiting Ratios of Generalized Recurrence Relations, Journal
11. P Senthil Kumar, R Abirami, A Dinesh Kumar, Fuzzy model for the effect of rhIL6 Infusion on Growth Hormone, International Conference on Advances in Applied Probability, Graph Theory and Fuzzy Mathematics, Vol. 252, 2014, pp. 246
12. P Senthil Kumar, A Dinesh Kumar, M Vasuki, Stochastic model to find the effect of gallbladder contraction result using uniform distribution, Arya Bhatta Journal of Mathematics and Informatics, Vol 6, No. 2, 2014, pp. 323 – 328
13. R. Sivaraman, Recognizing Ramanujan’s House Number Puzzle, German International Journal of Modern Science, 22, November 2021, pp. 25 – 27
14. R. Sivaraman, Pythagorean Triples and Generalized Recursive Sequences, Mathematical Sciences International Research Journal, Vol. 10, No. 2, July 2021, pp. 1 – 5
15. R. Sivaraman, Sum of powers of natural numbers, AUT AUT Research Journal, Volume XI, Issue IV, April 2020, pp. 353 – 359.
Downloads
Citation Tools
How to Cite
Vasuki, M., & Sivaraman, D. R. (2024). Solving Quadratic Diophantine Equation for Integral Powers of 37. International Journal Of Mathematics And Computer Research, 12(01), 3996-3998. https://doi.org/10.47191/ijmcr/v12i1.10