Abstract
Let x,yand z be non-negative integers. We solve the exponential Diophantine equation 2^x+1,245^y=z^2. The result indicates that the equation has a unique solution,(x,y,z)=(3,0,3).
References
Acu, D., (2007) On a Diophantine Equation, General Mathematics, 15(4), 145-148.
Aggarwal, S., Swarup, C., Gupta, D., and Kumar, S., (2023) Solution of the Diophantine Equation 143^x+85^y=z^2 , International Journal of Progressive Research in Science and Engineering, 4(02), 5 – 7.
Aggarwal, S., Kumar, S., Gupta, D., and Kumar, S., (2023) Solution of the Diophantine Equation 143^x+485^y=z^2 , International Research Journal of Modernization in Engineering Technology and Science, 5(02), 555 – 558.
Aggarwal, S., Pandey, R., and Kumar, S., (2024) Solution of the Exponential Diophantine Equation 10^x+400^y=z^2 , International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS), 8(2), 38 – 40.
Burshtein, N., (2019) On Solution to the Diophantine Equations 5^x+103^y=z^2 and 5^x+11^y=z^2 with Positive Integers x,y,z, Annals of Pure and Applied Mathematics, 19(1), 75-77.
Burton, D. M., (2011) Elementary Number Theory, Seventh Edition, The McGraw-Hill companies.
Jeyakrishnan, G. and Komahan, G., (2017) More on the Diophantine Equation 27^x+2^y=z^2, International Journal for Scientific Research & Development, 4(2), 166-167.
Kaewong, T., Thongnak, S.and Chuayjan, W., (2024) On the Exponential Diophantine Equation 305^x+503^y=z^2 , International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS), 8(2), 79 – 81.
Kumar, S. and Aggarwal, S., (2021) On the Exponential Diophantine Equation 439^p+457^q=r^2 , Journal of Emerging Technologies and innovative Research (JETIR), 8(3), 2357 –2361.
Mihailescu, P., (2004) Primary Cyclotomic Units and a Proof of Catalan’ s Conjecture, Journal fur die Reine und Angewandte
Mathematik, 572, 167–195.
Pakapongpun, A.and Chattae, B., (2022) On the Diophantine equation p^x+7^y=z^2, where pis Primes and x,y,z are non-negative integers, International Journal of Mathematics and Computer Science, 17(4), 1535-1540.
Sroysang, B., (2014) More on the Diophantine Equation 3^x+85^y=z^2, International Journal of Pure and Applied Mathematics, 91(1), 131-134.
Suvarnamani, A., (2011) On two Diophantine Equations 4^x+7^y=z^2and4^x+11^y=z^2, Science and Technology RMUTT Journal, 1(1), 25-28.
Tadee, S., (2022) On the Diophantine equation p^x+(p+14)^y=z^2where p,p+14are Primes, Annals of Pure and Applied Mathematics, 26(2), 125-130.
Viriyapong, N. and Viriyapong, C., (2023) On the Diophantine equation 255^x+323^y=z^2 , International Journal of Mathematics and Computer Science, 18(3), 521 – 523.
Viriyapong, N. and Viriyapong, C., (2024) On the Diophantine equation 147^x+741^y=z^2 , International Journal of Mathematics and Computer Science, 19(2), 445 – 447.