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n^n + 1 and (2n)^{2n} + 1 are both primes

Source: 7th QEDMO problem 1 (14. - 17. 1. 2010) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 9, 2021

number theoryprimes

Problem Statement

Find all natural numbers

n

for which both

n^n + 1

and

(2n)^{2n} + 1

are prime numbers.