We derive a Reid Roundabout Theorem for Sturm-Liouville Difference Equations of higher order by applying general results on linear Hamiltonian Difference Systems. This theorem gives conditions that are equivalent to the positive definiteness of a certain discrete quadratic functional; among them disconjugacy of the related Sturm-Liouville Difference Equation and solvability of a certain discrete Riccati Matrix Equation.

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