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Some number theoretic properties of arbitrary order recursive sequences

This thesis develops some number theoretic properties associated with sequences, the elements of which satisfy homogeneous linear recurrence relations of arbitrary order. The properties studied are those analogous to the results of Lucas [5] and A.F. Horadam [3] for the second order case, to examine their points of similarity. Their finite field properties have been developed extensively by Selmer [6] and there exists a fairly good knowledge of their global behaviour in terms of existence theorems, but knowledge of local behaviour in terms of reasonably elegant explicit and specific identities is limited.