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Algebraic integers with continued fraction expansions containing palindromes and square roots with prescribed periods

Algebraic integers with continued fraction expansions containing palindromes and square roots with prescribed periods

We prove that there exist infinitely many algebraic integers with continued fraction expansion of the kind $[a_0, \overline{a_1, \ldots, a_n, s}]$ where $(a_1, \ldots, a_n)$ is a palindrome and $s \in \mathbb N_{\geq1}$, characterizing all the algebraic integers with such expansions. We also provide an explicit method for finding $s$ …