Resumen de A note on the Diophantine equiation (ax - by)= c

Bo He, Alain Togbé, Shichun Yang

• Let a,b, and c be positive integers. We show that if (a,b)=(Nk−1,N), where N,k≥2, then there is at most one positive integer solution (x,y) to the exponential Diophantine equation |ax−by|=c, unless (N,k)=(2,2). Combining this with results of Bennett [3] and the first author [6], we stated all cases for which the equation |(Nk±1)x−Ny|=c has more than one positive integer solutions (x,y).