Prove that the equation x/y + y/z + z/x = 1 has no solutions in positive integers x, y, z.
Since x,y & z are positive, x/y, y/z & z/x are positive.
Therefore, 0<x/y<1 , 0<y/z<1 , 0<z/x<1
x/y<1 --> x<y
y/z<1 --> y<z --> x<y<z --> x<z --> z/x>1, which is a contradiction !