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Easy but nice NT with lcm

Source: ARO Regional stage 2023 9.6=10.6=11.6

February 16, 2023
number theoryleast common multipleRussia

Problem Statement

Does there exist a positive integer mm, such that if SnS_n denotes the lcm of 1,2,…,n1,2, \ldots, n, then Sm+1=4SmS_{m+1}=4S_m?
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