Solution of the Diophantine Equation 143^x + 45^y = z^2
Abstract
In this paper, authors studied the Diophantine equation, where are non-negative integers. The authors proved that is the unique non-negative integer solution of this Diophantine equation.
How to cite this article: Aggarwal S, Swarup C, Gupta D et al. Solution of the Diophantine Equation 143x + 45y = z2. J Adv Res Appl Math Stat 2022; 7(3&4): 1-4.
DOI: https://doi.org/10.24321/2455.7021.202205
References
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11. Mishra R, Aggarwal S, Kumar A. On the existence of solution of Diophantine equation 211ఈ + 229ఉ =γଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 78-79.
12. Goel P, Bhatnagar K, Aggarwal S. On the exponential Diophantine equation Mହ + M = rଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 170-171.
13. Bhatnagar K, Aggarwal S. On the exponential Diophantine equation 421 + 439 = rଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 128-129.
14. Kumar S, Bhatnagar K, Kumar A et al. On the exponential Diophantine equation (2ଶାଵ − 1) +(6ାଵ + 1) = ωଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 183-184.
15. Kumar S, Bhatnagar K, Kumar A et al. On the exponential Diophantine equation (7ଶ) + (6r + 1) =zଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 181-182.
16. Aggarwal S, Sharma N. On the non-linear Diophantine equation 379௫ + 397௬ = zଶ, Open Journal of Mathematical Sciences, 2020; 4(1): 397-399.
17. Aggarwal S. On the existence of solution of Diophantine equation 193௫ + 211௬ = zଶ, Journal of Advanced Research in Applied Mathematics and Statistics, 2020; 5(3&4): 4-5.
18. Aggarwal S, Kumar S. On the exponential Diophantine equation (13ଶ) + (6r + 1) = zଶ, Journal of Scientific Research, 2021; 13(3): 845-849.
19. Aggarwal S, Upadhyaya LM. On the Diophantine equation 8ఈ + 67ఉ = γଶ, Bulletin of Pure & Applied Sciences-Mathematics and Statistics, 2022; 41(2): 153-155.
20. Gupta D, Kumar S, Aggarwal S. Solution of non-linear exponential Diophantine equation (x + 1) +൫y + 1൯
= zଶ, Journal of Emerging Technologies and Innovative Research, 2022; 9(9): f154-f157.
21. Gupta D, Kumar S, Aggarwal S. Solution of non-linear exponential Diophantine equation xఈ +(1 + my)ఉ = z
ଶ, Journal of Emerging Technologies and Innovative Research, 2022; 9(9): d486-d489.
22. Schoof R. Catalan’s conjecture, Springer-Verlag, London 2008.
2. Sroysan B. On the Diophantine equation 323௫ + 325௬ = zଶ, International Journal of Pure and Applied Mathematics, 2014; 91(3): 395-398.
3. Sroysang B. On the Diophantine equation 3௫ + 45௬ = zଶ, International Journal of Pure and Applied Mathematics, 2014; 91(2): 269-272.
4. Sroysang B. On the Diophantine equation143௫ + 145௬ = zଶ, International Journal of Pure and Applied Mathematics, 2014; 91(2): 265-268.
5. Sroysang B. On the Diophantine equation 3௫ + 85௬ = zଶ, International Journal of Pure and Applied Mathematics, 2014; 91(1): 131-134.
6. Sroysang B. More on the Diophantine equation 4௫ + 10௬ = zଶ, International Journal of Pure and Applied Mathematics, 2014; 91(1): 135-138.
7. Hoque A, Kalita H. On the Diophantine equation (p − 1)௫ + p௬ = zଶ, Journal of Analysis & Number Theory, 2015; 3(2): 117-119.
8. Aggarwal S, Sharma SD, Singhal H. On the Diophantine equation 223௫ + 241௬ = zଶ, International Journal of Research and Innovation in Applied Science, 2020; 5(8): 155-156.
9. Aggarwal S, Sharma SD, Vyas A. On the existence of solution of Diophantine equation 181௫ +199௬ = zଶ, International Journal of Latest Technology in Engineering, Management & Applied Science, 2020; 9(8): 85-86.
10. Kumar A, Chaudhary L, Aggarwal S. On the exponential Diophantine equation 601 + 619 = rଶ, International Journal of Interdisciplinary Global Studies, (2020; 14(4): 29-30.
11. Mishra R, Aggarwal S, Kumar A. On the existence of solution of Diophantine equation 211ఈ + 229ఉ =γଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 78-79.
12. Goel P, Bhatnagar K, Aggarwal S. On the exponential Diophantine equation Mହ + M = rଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 170-171.
13. Bhatnagar K, Aggarwal S. On the exponential Diophantine equation 421 + 439 = rଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 128-129.
14. Kumar S, Bhatnagar K, Kumar A et al. On the exponential Diophantine equation (2ଶାଵ − 1) +(6ାଵ + 1) = ωଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 183-184.
15. Kumar S, Bhatnagar K, Kumar A et al. On the exponential Diophantine equation (7ଶ) + (6r + 1) =zଶ, International Journal of Interdisciplinary Global Studies, 2020; 14(4): 181-182.
16. Aggarwal S, Sharma N. On the non-linear Diophantine equation 379௫ + 397௬ = zଶ, Open Journal of Mathematical Sciences, 2020; 4(1): 397-399.
17. Aggarwal S. On the existence of solution of Diophantine equation 193௫ + 211௬ = zଶ, Journal of Advanced Research in Applied Mathematics and Statistics, 2020; 5(3&4): 4-5.
18. Aggarwal S, Kumar S. On the exponential Diophantine equation (13ଶ) + (6r + 1) = zଶ, Journal of Scientific Research, 2021; 13(3): 845-849.
19. Aggarwal S, Upadhyaya LM. On the Diophantine equation 8ఈ + 67ఉ = γଶ, Bulletin of Pure & Applied Sciences-Mathematics and Statistics, 2022; 41(2): 153-155.
20. Gupta D, Kumar S, Aggarwal S. Solution of non-linear exponential Diophantine equation (x + 1) +൫y + 1൯
= zଶ, Journal of Emerging Technologies and Innovative Research, 2022; 9(9): f154-f157.
21. Gupta D, Kumar S, Aggarwal S. Solution of non-linear exponential Diophantine equation xఈ +(1 + my)ఉ = z
ଶ, Journal of Emerging Technologies and Innovative Research, 2022; 9(9): d486-d489.
22. Schoof R. Catalan’s conjecture, Springer-Verlag, London 2008.
Published
2022-12-05
How to Cite
AGGARWAL, Sudhanshu et al.
Solution of the Diophantine Equation 143^x + 45^y = z^2.
Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 7, n. 3&4, p. 1-4, dec. 2022.
ISSN 2455-7021.
Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/704>. Date accessed: 02 jan. 2025.
Section
Research Article
