ON THE DIOPHANTINE EQUATION axy + byz + czx = 0.

Let a, b, c be integers. In this paper, we prove the integer solutions of the equation ax^y + by^z + cz^x = 0 satisfy max{|x|, |y|, |z|} ≤ 2 max{a, b, c} when a, b, c are odd positive integers, and when a = b = 1, c = -1, the positive integer solutions of the equation satisfy max{x, y, z} < exp(exp(exp(5))). [ABSTRACT FROM AUTHOR]