关于指数型丢番图方程的整数解

On Integer Solutions of Exponential Diophantine Equations

本文简要地介绍了有关Ｓ－单位方程、Ｒａｍａｎｕｊａｎ－Ｎａｇｅｌｌ方程、Ｔｈｕｅ－Ｍａｈｌｅｒ方程，ＬｅＶｅｑｕｅ方程、Ｃａｔａｌａｎ方程、Ｐｉｌｌａｉ方程等指数型丢番图方程整数解的最新结果。这些结果大多是用Ｔｈｕｅ－Ｓｉｅｇｌｅ－Ｒｏｔｈ－Ｓｃｈｍｉｄｔ方法和Ｇｅｌ’ｆｏｎｄ－Ｂａｋｅｒ方法得到的。

This paper is a brief introduction of some recent results concerninginteger solutions of exponential diophantine equations, such as S-unit equation,equationof Ramanujan-Nagell,of Thue-Mahler,of LeVeque,of Catalan,of Pillai.Most of theresults have been obtained by Thue-Siegle-Roth-Schmidt method and Gel 'fond-Bakermethod.