Glasnik matematički, Vol. 53 No. 2, 2018.
Izvorni znanstveni članak
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
orcid.org/0000-0002-5882-936X
; Department of Mathematics, Statistics, and Computer Science, Purdue University Northwest, 1401 S. U.S. 421 Westville, IN 46391
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
Hrčak ID:
214472
URI
Datum izdavanja:
30.12.2018.
Posjeta: 788 *