•  
  •  
 

Turkish Journal of Mathematics

Authors

MURAT ALAN

DOI

10.3906/mat-1801-76

Abstract

Let $m$ be a positive integer. We show that the exponential Diophantine equation $ (18m^2+1)^x+(7m^2-1)^y=(5m)^z $ has only the positive integer solution $(x,y,z)=(1,1,2)$ except for $m \equiv 23,47,63, 87 \pmod {120}$. For $m\not\equiv 0 \pmod5$ we use some elementary methods and linear forms in two logarithms. For $m \equiv 0 \pmod 5$ we apply a result for linear forms in $p$-adic logarithms.

First Page

1990

Last Page

1999

Included in

Mathematics Commons

Share

COinS