Question Number 180211 by Shrinava last updated on 09/Nov/22
$$\mathrm{Find}: \\ $$$$\Omega\:=\:\mathrm{gcd}\:\left(\mathrm{4}^{\mathrm{2020}} −\mathrm{1}\:,\:\mathrm{8}^{\mathrm{2021}} −\mathrm{1}\right).\:\mathrm{Generalization}. \\ $$
Answered by puissant last updated on 09/Nov/22
$$\Omega\:=\:{gcd}\left(\mathrm{2}^{\mathrm{4040}} −\mathrm{1}\:;\:\mathrm{2}^{\mathrm{6063}} −\mathrm{1}\right) \\ $$$$\:\:\:\:\:=\:\mathrm{2}^{{gcd}\left(\mathrm{4040}\:;\:\mathrm{6063}\right)} −\mathrm{1} \\ $$$$\:\:\:\:\:=\:\mathrm{2}^{\mathrm{1}} −\mathrm{1} \\ $$$$\:\:\:\:\:=\:\mathrm{1}. \\ $$