On the number of solutions of Goormaghtigh equation for given x and y

In this note, we extend a result obtained by Bugeaud and Shorey in Pacific J. Math.207 (2002) 61–75. In fact, we show that the Goormaghtigh equation xm−1x−1=yn−1y−1,x>1,y>1,m>1,n>1,x