Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 15 (2020), 473 -- 523

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This work is licensed under a Creative Commons Attribution 4.0 International License.

A BRIEF SURVEY ON THE GENERALIZED LEBESGUE-RAMANUJAN-NAGELL EQUATION

Maohua Le and Gökhan Soydan

Abstract. The generalized Lebesgue-Ramanujan-Nagell equation is an important type of polynomial-exponential Diophantine equation in number theory. In this survey, the recent results and some unsolved problems of this equation are given.

2020 Mathematics Subject Classification: 11D61
Keywords: polynomial-exponential Diophantine equation; generalized Lebesgue-Ramanujan-Nagell equation

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Maohua Le
Institute of Mathematics, Lingnan Normal College
Zhangjiang, Guangdong, 524048 China.
e-mail: lemaohua2008@163.com

Gökhan Soydan
Department of Mathematics,
Bursa Uludag University, 16059 Bursa, Turkey.
e-mail: gsoydan@uludag.edu.tr
http://gsoydan.home.uludag.edu.tr

http://www.utgjiu.ro/math/sma