let us assume that $x_1, x_2, x_3, x_4, y_1, y_2, y_3, y_4$ are integer numbers and $m$ is an rational number. i want to choose $m$ such that the following equation is never satisfied :
$$(x_1^2 + x_2^2 + x_3^2 + x_4^2 ) - m( y_1^2 + y_2^2 + y_3^2 + y_4^2 ) =0$$
note that $m$ must belong to rational numbers . whatever $m$ get more close to 1 , it is more appropriate for my problem.