A Characterization for the Length of Cycles of the N - Number Ducci Game
نویسندگان
چکیده
This article considers the n-number Ducci game as a linear map over the n dimensional vector space ZZn 2 . Period lengths are characterized as orders of factors of the minimal polynomial of that transformation. The minimal polynomial can be explicitly obtained for any n. We provide algebraic proofs of divisibility conditions, initially found by Ehrlich. In addition, all periodic cycle lengths for 3 n 40 are provided.
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