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Classical NT using modular arithmetic

Source: 2022 Turkey TST P1 Day 1 + 2023 Dutch BxMO TST, Problem 5

March 13, 2022
number theorymodular arithmeticnumber theory proposedDiophantine equation

Problem Statement

Find all pairs of prime numbers (p,q)(p,q) for which 2p=2qāˆ’2+q!.2^p = 2^{q-2} + q!.
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