TR-MO-R1 2022 Problem 6

$a_1 = 12$ ve her $n = 1, 2, \ldots, 2021$ için $a_{n+1} = 12^{a_n}$ koşulunu sağlayan bir $(a_n)$ tam sayı dizisi tanımlanıyor. $a_{2022}$ sayısının 67 ile bölümünden kalan kaçtır?

a) 1 b) 4 c) 9 d) 16 e) 25

Official text Turkish Mathematical Olympiad, first round 2022 official paper, page 5. Quoted with source.

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