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Wall published a paper in 1960 on the Fibonacci sequence where he derivedmany results concerning the period and prime power divisibility modulo m. Hisperiodicity results have been generalized to second order linear recurrences.Here we study the sequences generated by such recurrences, with starting valuesof {0,1}: among other things, we derive new prime power divisibility results,derive the period by new methods, establish new identities, show derivationsinvolving powers of matrices generated by these general recurrences, etc.

Prime Power Divisibility,Periodicity and Other Properties of Some Second Order Recurrences