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Relatively Prime Construction

Source: Indonesian Stage 1 TST for IMO 2022, Test 1 (Number Theory)

December 11, 2021
number theoryrelatively prime

Problem Statement

Prove that there exists a set X⊆NX \subseteq \mathbb{N} which contains exactly 2022 elements such that for every distinct a,b,c∈Xa, b, c \in X the following equality: gcd⁡(an+bn,c)=1 \gcd(a^n+b^n, c) = 1 is satisfied for every positive integer nn.
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