Solution of the Diophantine Equation ðŸðŸŽð’™+ðŸ’ðŸŽð’š=ð’›ðŸ
Abstract
Researchers are becoming more interested in creating new methods for dissecting the nature and solutions of the various Diophantine equations because Diophantine equations are so crucial in resolving significant real-world issues like network flow problems, pole placement problems, business investment problems, and data privacy problems. This study's authors researched the Diophantine problem 10ð‘¥+40ð‘¦=ð‘§2, where ð‘¥,ð‘¦,𑧠are non-negative integers, and discovered that it has no non-negative integer solution.
References
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2. Aggarwal, S., Sharma, S.D. and Singhal, H. (2020) On the Diophantine equation 223ð‘¥+241ð‘¦=ð‘§2, International Journal of Research and Innovation in Applied Science, 5 (8), 155-156.
3. Aggarwal, S., Sharma, S.D. and Vyas, A. (2020) On the existence of solution of Diophantine equation 181ð‘¥+199ð‘¦=ð‘§2, International Journal of Latest Technology in Engineering, Management & Applied Science, 9 (8), 85-86.
4. Aggarwal, S. and Sharma, N. (2020) On the non-linear Diophantine equation 379ð‘¥+397ð‘¦=ð‘§2, Open Journal of Mathematical Sciences, 4(1), 397-399.
5. Aggarwal, S. (2020) On the existence of solution of Diophantine equation 193ð‘¥+211ð‘¦=ð‘§2, Journal of Advanced Research in Applied Mathematics and Statistics, 5(3 & 4), 4-5.
6. Hoque, A. and Kalita, H. (2015) On the Diophantine equation (ð‘ð‘žâˆ’1)ð‘¥+ð‘ð‘žð‘¦=ð‘§2, Journal of Analysis & Number Theory, 3(2), 117-119.
7. Kumar, A., Chaudhary, L. and Aggarwal, S. (2020) On the exponential Diophantine equation 601ð‘+619ð‘ž=ð‘Ÿ2, International Journal of Interdisciplinary Global Studies, 14(4), 29-30.
8. Kumar, S., Bhatnagar, K., Kumar, A. and Aggarwal, S. (2020) On the exponential Diophantine equation (22ð‘š+1−1)+(6ð‘Ÿ+1+1)ð‘›=ðœ”2, International Journal of Interdisciplinary Global Studies, 14(4), 183-184.
9. Bhatnagar, K. and Aggarwal, S. (2020) On the exponential Diophantine equation 421ð‘+439ð‘ž=ð‘Ÿ2, International Journal of Interdisciplinary Global Studies, 14(4), 128-129.
10. Gupta, D., Kumar, S. and Aggarwal, S. (2022) Solution of non-linear exponential Diophantine equation(ð‘¥ð‘Ž+1)ð‘š+(ð‘¦ð‘+1)ð‘›=ð‘§2, Journal of Emerging Technologies and Innovative Research, 9(9), f154-f157.
11. Gupta, D., Kumar, S. and Aggarwal, S. (2022) Solution of non-linear exponential Diophantine equation ð‘¥ð›¼+(1+ð‘šð‘¦)ð›½=ð‘§2, Journal of Emerging Technologies and Innovative Research, 9(9), d486-d489.
12. Aggarwal, S. and Kumar, S. (2021) On the exponential Diophantine equation (132ð‘š)+(6ð‘Ÿ+1)ð‘›=ð‘§2, Journal of Scientific Research, 13(3), 845-849.
13. Aggarwal, S. and Upadhyaya, L.M. (2022) On the Diophantine equation 8ð›¼+67ð›½=ð›¾2, Bulletin of Pure & Applied Sciences-Mathematics and Statistics, 41(2), 153-155.
14. Goel, P., Bhatnagar, K. and Aggarwal, S. (2020) On the exponential Diophantine equation ð‘€5ð‘+ð‘€7ð‘ž=ð‘Ÿ2, International Journal of Interdisciplinary Global Studies, 14(4), 170-171.
15. Kumar, S., Bhatnagar, K., Kumar, N. and Aggarwal, S. (2020) On the exponential Diophantine equation
(72ð‘š)+(6ð‘Ÿ+1)ð‘›=ð‘§2, International Journal of Interdisciplinary Global Studies, 14(4), 181-182.
16. Mishra, R., Aggarwal, S. And Kumar, A. (2020) On the existence of solution of Diophantine equation 211ð›¼+229ð›½=ð›¾2, International Journal of Interdisciplinary Global Studies, 14(4), 78-79.
17. Schoof, R. (2008) Catalan’s conjecture, Springer-Verlag, London.
18. Sroysang, B. (2014) On the Diophantine equation 323ð‘¥+325ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(3), 395-398.
19. Sroysang, B. (2014) On the Diophantine equation 3ð‘¥+45ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(2), 269-272.
20. Sroysang, B. (2014) On the Diophantine equation143ð‘¥+145ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(2), 265-268.
21. Sroysang, B. (2014) On the Diophantine equation 3ð‘¥+85ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(1), 131-134.
22. Sroysang, B. (2014) More on the Diophantine equation 4ð‘¥+10ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(1), 135-138.
23. Aggarwal, S., Swarup, C., Gupta, D. and Kumar, S. (2022) Solution of the Diophantine equation 143ð‘¥+45ð‘¦=ð‘§2, Journal of Advanced Research in Applied Mathematics and Statistics, 7(3 & 4), 1-4.
24. Aggarwal, S., Kumar, S., Gupta, D. and Kumar, S. (2023) Solution of the Diophantine equation 143ð‘¥+485ð‘¦=ð‘§2, International Research Journal of Modernization in Engineering Technology and Science, 5(2), 555-558.
25. Aggarwal, S., Swarup, C., Gupta, D. and Kumar, S. (2023) Solution of the Diophantine equation 143ð‘¥+85ð‘¦=ð‘§2, International Journal of Progressive Research in Science and Engineering, 4(2), 5-7.
26. Aggarwal, S., Shahida A.T., Pandey, E. and Vyas, A. (2023) On the problem of solution of non-linear (exponential) Diophantine equation βð‘¥+(β+18)ð‘¦=ð‘§2, Mathematics and Statistics, 11(5), 834-839
2. Aggarwal, S., Sharma, S.D. and Singhal, H. (2020) On the Diophantine equation 223ð‘¥+241ð‘¦=ð‘§2, International Journal of Research and Innovation in Applied Science, 5 (8), 155-156.
3. Aggarwal, S., Sharma, S.D. and Vyas, A. (2020) On the existence of solution of Diophantine equation 181ð‘¥+199ð‘¦=ð‘§2, International Journal of Latest Technology in Engineering, Management & Applied Science, 9 (8), 85-86.
4. Aggarwal, S. and Sharma, N. (2020) On the non-linear Diophantine equation 379ð‘¥+397ð‘¦=ð‘§2, Open Journal of Mathematical Sciences, 4(1), 397-399.
5. Aggarwal, S. (2020) On the existence of solution of Diophantine equation 193ð‘¥+211ð‘¦=ð‘§2, Journal of Advanced Research in Applied Mathematics and Statistics, 5(3 & 4), 4-5.
6. Hoque, A. and Kalita, H. (2015) On the Diophantine equation (ð‘ð‘žâˆ’1)ð‘¥+ð‘ð‘žð‘¦=ð‘§2, Journal of Analysis & Number Theory, 3(2), 117-119.
7. Kumar, A., Chaudhary, L. and Aggarwal, S. (2020) On the exponential Diophantine equation 601ð‘+619ð‘ž=ð‘Ÿ2, International Journal of Interdisciplinary Global Studies, 14(4), 29-30.
8. Kumar, S., Bhatnagar, K., Kumar, A. and Aggarwal, S. (2020) On the exponential Diophantine equation (22ð‘š+1−1)+(6ð‘Ÿ+1+1)ð‘›=ðœ”2, International Journal of Interdisciplinary Global Studies, 14(4), 183-184.
9. Bhatnagar, K. and Aggarwal, S. (2020) On the exponential Diophantine equation 421ð‘+439ð‘ž=ð‘Ÿ2, International Journal of Interdisciplinary Global Studies, 14(4), 128-129.
10. Gupta, D., Kumar, S. and Aggarwal, S. (2022) Solution of non-linear exponential Diophantine equation(ð‘¥ð‘Ž+1)ð‘š+(ð‘¦ð‘+1)ð‘›=ð‘§2, Journal of Emerging Technologies and Innovative Research, 9(9), f154-f157.
11. Gupta, D., Kumar, S. and Aggarwal, S. (2022) Solution of non-linear exponential Diophantine equation ð‘¥ð›¼+(1+ð‘šð‘¦)ð›½=ð‘§2, Journal of Emerging Technologies and Innovative Research, 9(9), d486-d489.
12. Aggarwal, S. and Kumar, S. (2021) On the exponential Diophantine equation (132ð‘š)+(6ð‘Ÿ+1)ð‘›=ð‘§2, Journal of Scientific Research, 13(3), 845-849.
13. Aggarwal, S. and Upadhyaya, L.M. (2022) On the Diophantine equation 8ð›¼+67ð›½=ð›¾2, Bulletin of Pure & Applied Sciences-Mathematics and Statistics, 41(2), 153-155.
14. Goel, P., Bhatnagar, K. and Aggarwal, S. (2020) On the exponential Diophantine equation ð‘€5ð‘+ð‘€7ð‘ž=ð‘Ÿ2, International Journal of Interdisciplinary Global Studies, 14(4), 170-171.
15. Kumar, S., Bhatnagar, K., Kumar, N. and Aggarwal, S. (2020) On the exponential Diophantine equation
(72ð‘š)+(6ð‘Ÿ+1)ð‘›=ð‘§2, International Journal of Interdisciplinary Global Studies, 14(4), 181-182.
16. Mishra, R., Aggarwal, S. And Kumar, A. (2020) On the existence of solution of Diophantine equation 211ð›¼+229ð›½=ð›¾2, International Journal of Interdisciplinary Global Studies, 14(4), 78-79.
17. Schoof, R. (2008) Catalan’s conjecture, Springer-Verlag, London.
18. Sroysang, B. (2014) On the Diophantine equation 323ð‘¥+325ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(3), 395-398.
19. Sroysang, B. (2014) On the Diophantine equation 3ð‘¥+45ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(2), 269-272.
20. Sroysang, B. (2014) On the Diophantine equation143ð‘¥+145ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(2), 265-268.
21. Sroysang, B. (2014) On the Diophantine equation 3ð‘¥+85ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(1), 131-134.
22. Sroysang, B. (2014) More on the Diophantine equation 4ð‘¥+10ð‘¦=ð‘§2, International Journal of Pure and Applied Mathematics, 91(1), 135-138.
23. Aggarwal, S., Swarup, C., Gupta, D. and Kumar, S. (2022) Solution of the Diophantine equation 143ð‘¥+45ð‘¦=ð‘§2, Journal of Advanced Research in Applied Mathematics and Statistics, 7(3 & 4), 1-4.
24. Aggarwal, S., Kumar, S., Gupta, D. and Kumar, S. (2023) Solution of the Diophantine equation 143ð‘¥+485ð‘¦=ð‘§2, International Research Journal of Modernization in Engineering Technology and Science, 5(2), 555-558.
25. Aggarwal, S., Swarup, C., Gupta, D. and Kumar, S. (2023) Solution of the Diophantine equation 143ð‘¥+85ð‘¦=ð‘§2, International Journal of Progressive Research in Science and Engineering, 4(2), 5-7.
26. Aggarwal, S., Shahida A.T., Pandey, E. and Vyas, A. (2023) On the problem of solution of non-linear (exponential) Diophantine equation βð‘¥+(β+18)ð‘¦=ð‘§2, Mathematics and Statistics, 11(5), 834-839
Published
2023-12-15
How to Cite
AGGARWAL, Sudhanshu; A.T., Shahida.
Solution of the Diophantine Equation ðŸðŸŽð’™+ðŸ’ðŸŽð’š=ð’›ðŸ.
Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 8, n. 3&4, p. 26-29, dec. 2023.
ISSN 2455-7021.
Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/928>. Date accessed: 02 jan. 2026.
Section
Research Article
