MathDB

Let

S

be a non-empty set of positive integers such that for any

n \in S

, all positive divisors of

2^n+1

are also in

S

. Prove that

S

contains an integer of the form

(p_1p_2 \ldots p_{2023})^{2023}

, where

p_1, p_2, \ldots, p_{2023}

are distinct prime numbers, all greater than

2023

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