On the exponential Diophantine equation $a^x + l^y = c^z$

Nobuhiro Terai

Type: Article

Publication Date: 2001-11-01

Citations: 2

DOI: https://doi.org/10.3792/pjaa.77.151

Abstract

Using the theory of linear forms in logarithms and a result due to Adachi, we show that the title equation has only the trivial positive integral solution under some conditions.

Locations

Proceedings of the Japan Academy Series A Mathematical Sciences - View - PDF

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Works Cited by This (9)

Action	Title	Year	Authors
+	Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations	1999	Nobuhiro Terai
+	Diophantine eaquations of the form ax2 + Db2 = yp.	1977	Ezra Brown
+	On the Equations px − by = c and ax + by = cz	1993	Reese Scott
+	Formes linéaires en deux logarithmes et déterminants d′interpolation	1995	Laurent Michel Maurice Mignotte Yuri Valentinovich Nesterenko
+ PDF Chat	On the Diophantine equation<i>Cx</i><sup>2</sup>+<i>D</i>=<i>y</i><sup><i>n</i></sup>	1964	W. Ljunggren
+ PDF Chat	The Diophantine Equation $x^2\pm ly^2=z^l$ Connected with Fermat's Last Theorem	1988	Norio Adachi
+	Diophantine equations of the form x2 + D = yn.	1975
+ PDF Chat	A corollary to a theorem of Laurent-Mignotte-Nesterenko	1998	Max Mignotte
+ PDF Chat	A note on the Diophantine equation $a^x + b^y = c^z$	1999	Zhenfu Cao