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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 $s$ …