A Division Algorithm Approach to $p$-Adic Sylvester Expansions

Eric Errthum

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arXiv · 1508.01503

A Division Algorithm Approach to $p$-Adic Sylvester Expansions

Eric Errthum

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Abstract

A method of constructing finite $p$-adic Sylvester expansions for all rationals is presented. This method parallels the classical Fibonacci-Sylvester (greedy) algorithm by iterating a $p$-adic division algorithm. The method extends to irrational $p$-adics that have an embedding in the reals.

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Eric Errthum. 2015-08-06. A Division Algorithm Approach to $p$-Adic Sylvester Expansions. https://arxiv.org/abs/1508.01503

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