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sets of prime numbers

Source: 12th Dürer Math Competition ,First Round, Category E+, P2

August 18, 2020
number theoryprime numbers

Problem Statement

For a positive integer nn let P(n)P(n) denote the set of primes pp for which there exist positive integers a,ba, b such that n=ap+bpn=a^p+b^p . Is it true that for any finite set HH consisting of primes, there is an n such that P(n)=HP(n) = H?
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