Positive integer solutions of the diophantine equation: X2 -lnxy +(-1)ny2 = ±5r

Abstract

In this paper, we consider the equation X2 -lnxy +(-1)ny2 = ±5r and determine the values of n for which the equation has positive integer solutionsx and y. Moreover, we give all positive integer solutions of the equation X2 -lnxy +(-1)ny2 = ±5r when the equation has positive integer solutions. © Indian Academy of Sciences.