On the period of the continued fraction expansion of ${\sqrt {2^{2n+1}+1}}$

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69962In this paper, we prove that the period of the continued fraction expansion of ${\sqrt {2^{n}+1}}$ tends to infinity when $n$ tends to infinity through odd positive integers.Number Theory11J70, 11J25On the period of the continued fraction expansion of ${\sqrt {2^{2n+1}+1}}$text