XiGeng Chen(1),MaoHua Le(2)
Let n be a positive integer. In this paper, under the assumption of the generalized Riemann conjecture, we prove that if and only if n =1,2,4,6,10,18,22,30,42,58, 70,78,102,130,190,210,330,462, then the equation xy+yz+zx=n has no positive integer solution (x,y,z) .