I'm trying to find out for which natural numbers $n$, does $9^n + 1$ have all of its prime factors less than $40$. If I can provide a positive answer to my title question, then I will have a proof that only $n = 1$ causes $9^n + 1$ to have all of its prime factors less than $40$. Thank you for any help.
Does $9^{2^n} + 1$ always have a prime factor larger than $40$?
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number-theory