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Sequence with gcd and lcm

Source: Latvian TST for Baltic Way 2020 P16

October 18, 2020

number theoryleast common multiplegreatest common divisor

Problem Statement

Given sequence

\{a_n\}

satisfying:

a_{n+1} = \frac{ lcm(a_n,a_{n-1})}{\gcd(a_n, a_{n-1})}

It is given that

a_{209} =209

and

a_{361} = 361

. Find all possible values of

a_{2020}