Question 65
Let $a_1, a_2, \dots, a_n$ be the sequence of positive integers. For each number $\ell$ from $1$ to $n-1$ the following collection was found:
$$(\gcd(a_1, a_{1+\ell}), \gcd(a_2, a_{2+\ell}), \dots, \gcd(a_n, a_{n+\ell})),$$
where all indices are taken modulo $n$, i.e. if $s \gt n$ then $a_s = a_{s-n}$. It turned out that all these collections consist of the same $n$ pairwise distinct numbers maybe in different ordering.
Find out if $n$ can be equal to a) $21$; b) $2021$.
$$(\gcd(a_1, a_{1+\ell}), \gcd(a_2, a_{2+\ell}), \dots, \gcd(a_n, a_{n+\ell})),$$
where all indices are taken modulo $n$, i.e. if $s \gt n$ then $a_s = a_{s-n}$. It turned out that all these collections consist of the same $n$ pairwise distinct numbers maybe in different ordering.
Find out if $n$ can be equal to a) $21$; b) $2021$.