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composition of sets of form 2^{2^n}+1 and 6^{2^n}+1 is finite

Source: 2006 VMEO III Shortlist SL N11 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__vie

October 28, 2021
number theorypowers

Problem Statement

Prove that the composition of the sets of one of the following two forms is finite: (a) 22n+12^{2^n}+1 (b) 62n+16^{2^n}+1