The equation x1/x2 + x2/x3 + x3/x4 + x4/x1 = n

It is a subtle question as to when the Diophantine equation of the tittle has solutions in positive integers. Here, we show that the equation in the title does not have solutions in positive integers in the case that n is of the form n = 4q, where q(2) - 1 = 2(h)q(1), with h, q(1) is an element of Z(+), 2 vertical bar h, h >= 4, and 8 vertical bar q(1) + 1. We do this by explicitly calculating a Brauer-Manin obstruction to weak approximation on the elliptic surface defined by the title equation.