A PURE EXPONENTIAL DIOPHANTINE EQUATION

摘要

Let u be an even integer. In this paper we prove that if 4|u and u >208, then the equation (u~3 - 3u)~x +(3u~2 - 1)~y =(u~2 +1)~z has only the positive integer solution (x,y,z) =(2,2,3). This result basically determine all solutions of the equation.