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A direct method to construct polynomial integrals for third order ordinary difference equation (OΔE) w(n + 3) = F(w(n), w(n + 1),w(n + 2)) and fourth order OΔE w(n + 4) = F(w(n), w(n + 1), w(n + 2), w(n + 3)) is presented. The effectiveness of the method to construct more than one polynomial integral for N-th order OΔE is also briefly discussed.

Polynomial integrals for third- and fourth-order ordinary difference equations