On the period of the continued fraction expansion of √ 2²ⁿ⁺¹+1

2004/01/26 by Yann Bugeaud, Florian Luca, Bugeaud, Yann +1
Mathematics · #11J25 #11J70 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J25 #msc:11J70

paper · pdf · doi:10.48550/arxiv.math/0401341

arxiv created 2004/01/26 · arxiv updated 2009/12/01

Abstract

In this paper, we prove that the period of the continued fraction expansion of √ 2ⁿ+1 tends to infinity when n tends to infinity through odd positive integers.

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