ON THE DIOPHANTINE EQUATION 9^x+9^y+n^z=w^2
คำสำคัญ:
Diophantine equation, Integer solution, Congruenceบทคัดย่อ
In this work, we give some conditions for the non-existence of solutions of the Diophantine equation , where
is a positive integer and
are non-negative integers. Moreover, we find all solutions of this equation for some positive integer
.
References
Asthana, S. & Singh, M.M. (2020). On the Diophantine equation 3^x+117^y=z^2. GANITA, 70(2), 43-47.
Bacani, J. B. & Rabago, J. F. T. (2014). On the Diophantine equation 3^x+5^y+7^z=w^2. Konuralp Journal of Mathematics. 2(2), 64-69.
Burshtein, N. (2020). Solutions of the Diophantine equations p^x+〖(p+1)〗^y+〖(p+2)〗^z=M^2 for primes p≥2 when 1≤x,y,z≤2. Annals of Pure and Applied Mathematics. 22(1), 41-49.
Chotchaisthit, S. (2012). On the Diophantine equation 4^x+p^y=z^2 where p is a prime number. American Journal of Mathematics and Sciences. 1(1), 191-193.
Pandichelvi, V. & Sandhya, P. (2022). Investigation of solutions to an exponential Diophantine equation p_1^x+p_2^y+p_3^z=M^2 for prime triplets (p_1,p_2,p_3 ). International Journal of Scientific Research and Engineering Development. 5(2), 22-31.
Siraworakun, A. & Tadee, S. (2023). Solutions of the Diophantine equation p^x+q^y=z^2, where p,q≡3 (mod 4). International Journal of Mathematics and Computer Science. 18(1): 131-136.
Sroysang, B. (2014). More on the Diophantine equation 4^x+10^y=z^2. International Journal of Pure and Applied Mathematics. 91(1). 135-138.
Tadee, S. (2023). On the Diophantine equation n^x+10^y=z^2. WSEAS Transactions on Mathematics. 22, 150-153.
Tangjai, W. & Chubthaisong, C. (2021). On the Diophantine equation 3^x+p^y=z^2 where p≡2 (mod 3). WSEAS Transactions on Mathematics. 20, 283-287.
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