On periodic sequences for algebraic numbers

Details On periodic sequences for algebraic numbers On periodic sequences for algebraic numbers

1999-06-02

arxiv.org/abs/math/9906016v3

Mathematics

Number Theory

22 pages. An error in section five of the original paper has been corrected, resulting in some slight alterations in the state

Scientific paper

For each positive integer n greater than or equal to 2, a new approach to expressing real numbers as sequences of nonnegative integers is given. The n=2 case is equivalent to the standard continued fraction algorithm. For n=3, it reduces to a new iteration of the triangle. Cubic irrationals that are roots of x^3 + k x^2 + x - 1 are shown to be precisely those numbers with purely periodic expansions of period length one. For general positive integers n, it reduces to a new iteration of an n dimensional simplex.

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