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We present a direct algorithm for computing hypergeometric solutions of systems of linear difference equations and discuss applications to finding d'th order (d>=2) right-hand factors of a given linear difference operator with polynomial coefficients. This talk is based on a joint work with Mark van Hoeij, Johannes Middeke and Yi Zhou. Here is the link to "Hypergeometric solutions of linear difference systems": https://www.sciencedirect.com/science/article/pii/S0747717125000574