Involve: A Journal of Mathematics
- Volume 3, Number 2 (2010), 129-148.
Recursive sequences and polynomial congruences
We consider the periodicity of recursive sequences defined by linear homogeneous recurrence relations of arbitrary order, when they are reduced modulo a positive integer . We show that the period of such a sequence with characteristic polynomial can be expressed in terms of the order of as a unit in the quotient ring . When is prime, this order can be described in terms of the factorization of in the polynomial ring . We use this connection to develop efficient algorithms for determining the factorization types of monic polynomials of degree in .
Involve, Volume 3, Number 2 (2010), 129-148.
Received: 29 October 2007
Accepted: 26 January 2010
First available in Project Euclid: 20 December 2017
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Lehman, J.; Triola, Christopher. Recursive sequences and polynomial congruences. Involve 3 (2010), no. 2, 129--148. doi:10.2140/involve.2010.3.129. https://projecteuclid.org/euclid.involve/1513733291