Surveys in Mathematics and its Applications


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Volume 14 (2019), 109 -- 140

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A SURVEY ON THE TERNARY PURELY EXPONENTIAL DIOPHANTINE EQUATION ax + by = cz

Maohua Le, Reese Scott and Robert Styer

Abstract. Let a, b, c be fixed coprime positive integers with \min\a,b,c\>1. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions (x,y,z) of the ternary purely exponential diophantine equation ax + by = cz.

2010 Mathematics Subject Classification: 11D61.
Keywords: ternary purely exponential diophantine equation; Jesmanowicz conjecture, Terai-Jesmanowicz conjecture.

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

Reese Scott
Somerville, MA, USA.

Robert Styer
Department of Mathematics and Statistics,
Villanova University,
800 Lancaster Avenue
Villanova, PA 19085 USA.
e-mail: robert.styer@villanova.edu
http://www41.homepage.villanova.edu/robert.styer/

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