On the Triple Laplace- Sumudu-Elzaki Transform and Their Properties

Sudhanshu  Aggarwal; Tarig M  Elzaki

doi:10.48165/

Authors

Sudhanshu Aggarwal Department of Mathematics, Almanhal Academy of Science, Khartoum, Sudan.
Tarig M Elzaki Mathematics Department, Faculty of Sciences and Arts-Alkamil, King Abdulaziz University, Jeddah Saudi Arabia

DOI:

https://doi.org/10.48165/

Keywords:

Diophantine Equation, Catalan Conjecture, Solution, Integers

Abstract

In this paper, authors have examined the Diophantine equation 8a + 67f3 = y , where a, {3, y are non-negative integers, for non-negative integer solutions. Authors used Catalan’s conjecture for this purpose. Results of the present paper show that the Diophantine equation 8a + 67f3 = y , where a, {3, y are non-negative integers, has a unique solution in non-negative integers and this solution is given by (a, {3, y) = (1, 0, 3).

References

Andreescu, T. and Andrica, D. (2002). An introduction to Diophantine equations, GIL Publishing House, ISBN 973-9238-88-2.

Mordell, L.J. (1969). Diophantine equations, Academic Press, London, New York.

Sierpinski, W. (1988). Elementary theory of numbers, 2nd edition, North-Holland, Amsterdam.

Koshy, T. (2007). Elementary number theory with applications, Academic Press, 2nd edition, Amsterdam, Boston.

Sroysang, B. (2012). More on the Diophantine equation 8 + 19 = , International Journal of Pure and Applied Mathematics, 81(4), 601-604.

Sroysang, B. (2012). On the Diophantine equation 31 + 32 = , International Journal of Pure and Applied Mathematics, 81(4), 609-612.

Sroysang, B. (2014). On the Diophantine equation 8 + 13 = , International Journal of Pure and Applied Mathematics, 90(1), 69-72.

Aggarwal, S. (2020). On the existence of solution of Diophantine equation 193 + 211 = , Journal of Advanced Research in Applied Mathematics and Statistics, 5(3&4), 1-2.

Aggarwal, S. and Sharma, N. (2020). On the non-linear Diophantine equation 379 + 397 = , Open Journal of Mathematical Sciences, 4(1), 397-399. DOI: 10.30538/oms2020.0129

Bhatnagar, K. and Aggarwal, S. (2020). On the exponential Diophantine equation 421 + 439 = ,

International Journal of Interdisciplinary Global Studies, 14(4), 128-129.

Gupta, D., Kumar, S. and Aggarwal, S. (2022). Solution of non-linear exponential Diophantine equation ( + 1) + ( + 1) = , Journal of Emerging Technologies and Innovative Research, 9(9), f154- f157.

Gupta, D., Kumar, S. and Aggarwal, S. (2022). Solution of non-linear exponential Diophantine equation

a + (1 + )f3 = , Journal of Emerging Technologies and Innovative Research, 9(9), d486-d489.

Schoof, R. (2008). Catalan’s conjecture, Springer-Verlag, London.