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https://doi.org/10.3336/gm.53.2.01

On the Ramanujan-Nagell type Diophantine equation x2+Akn=B

Zhongfeng Zhang ; School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
Alain Togbé ; Department of Mathematics, Statistics, and Computer Science, Purdue University Northwest, 1401 S. U.S. 421 Westville, IN 46391

Puni tekst: engleski, pdf (109 KB) str. 221-228 preuzimanja: 237* citiraj
APA 6th Edition
Zhang, Z. i Togbé, A. (2018). On the Ramanujan-Nagell type Diophantine equation x2+Akn=B. Glasnik matematički, 53 (2), 221-228. https://doi.org/10.3336/gm.53.2.01
MLA 8th Edition
Zhang, Zhongfeng i Alain Togbé. "On the Ramanujan-Nagell type Diophantine equation x2+Akn=B." Glasnik matematički, vol. 53, br. 2, 2018, str. 221-228. https://doi.org/10.3336/gm.53.2.01. Citirano 25.10.2021.
Chicago 17th Edition
Zhang, Zhongfeng i Alain Togbé. "On the Ramanujan-Nagell type Diophantine equation x2+Akn=B." Glasnik matematički 53, br. 2 (2018): 221-228. https://doi.org/10.3336/gm.53.2.01
Harvard
Zhang, Z., i Togbé, A. (2018). 'On the Ramanujan-Nagell type Diophantine equation x2+Akn=B', Glasnik matematički, 53(2), str. 221-228. https://doi.org/10.3336/gm.53.2.01
Vancouver
Zhang Z, Togbé A. On the Ramanujan-Nagell type Diophantine equation x2+Akn=B. Glasnik matematički [Internet]. 2018 [pristupljeno 25.10.2021.];53(2):221-228. https://doi.org/10.3336/gm.53.2.01
IEEE
Z. Zhang i A. Togbé, "On the Ramanujan-Nagell type Diophantine equation x2+Akn=B", Glasnik matematički, vol.53, br. 2, str. 221-228, 2018. [Online]. https://doi.org/10.3336/gm.53.2.01

Sažetak
Let A, B be positive integers and q a prime. In this paper, we prove that the Ramanujan-Nagell type Diophantine equation x2+Aqn=B has at most four nonnegative integer solutions (x, n) for q2∤ B and B≥ C where C is some constant depending of A. We also prove that the equation x2+3×2n=B has at most four nonnegative integer solutions (x, n). Therefore, we partially confirm a conjecture of Ulas ([4]).

Ključne riječi
Diophantine equations

Hrčak ID: 214472

URI
https://hrcak.srce.hr/214472

Posjeta: 379 *