A number theory problem by Vitor Santos

x,y,z,tx,y,z,t are all integers satisfying the following system of equations: {xz2yt=3xt+yz=1. \begin{cases} \begin{aligned} xz-2yt&=3 \\ xt+yz&=1. \end{aligned} \end{cases} Find x2+y2+z2+t2 x^2+y^2+z^2+ t^2 .

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