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Primes with difference 2 dividing 2^n-1

Source: German TST 2023 AIMO 3, Problem 1

November 2, 2023
power of 2number theoryprimes

Problem Statement

Does there exist a positive odd integer nn so that there are primes p1p_1, p2p_2 dividing 2n−12^n-1 with p1−p2=2p_1-p_2=2?
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