On the periods of generalized Fibonacci recurrences

Details On the periods of generalized Fibonacci recurrences On the periods of generalized Fibonacci recurrences

2010-04-30

arxiv.org/abs/1004.5439v1

Mathematics of Computation 63 (1994), 389-401.

Mathematics

Number Theory

13 pages. An old Technical Report, submitted for archival purposes. For further details, see http://wwwmaths.anu.edu.au/~brent

Scientific paper

We give a simple condition for a linear recurrence (mod 2^w) of degree r to have the maximal possible period 2^(w-1).(2^r-1). It follows that the period is maximal in the cases of interest for pseudo-random number generation, i.e. for 3-term linear recurrences defined by trinomials which are primitive (mod 2) and of degree r > 2. We consider the enumeration of certain exceptional polynomials which do not give maximal period, and list all such polynomials of degree less than 15.

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