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Define the sequence a_1, a_2, a_3, ... as follows. a_1 and a_2 are coprime positive integers and a_{n + 2} = a_{n + 1}a_n + 1. Show that for every m > 1 there is an n > m such that a_m^m divides a_n^n. Is it true that a_1 must divide a_n^n for some n > 1?

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