On length of the period of the continued fraction of n√(d)

2021/06/05 by Gawron, Filip, Kobos, Tomasz
#FOS: Mathematics #Number Theory (math.NT) #Primary 11A55

paper · doi:10.48550/arxiv.2106.02895

Abstract

For a given quadratic irrational α, let us denote by D(α) the length of the periodic part of the continued fraction expansion of α. We prove that for a positive integer d, which is not a perfect square, the sequence (D(n√(d)))_n=1^∞ has infinitely many limit points.

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