Question 66
For a given positive integer $n$ one has to choose positive integers $a_0, a_1, \dots$ so that the following conditions hold:
(1) $a_i = a_{i+n}$ for any $i$;
(2) $a_i$ is not divisible by $n$ for any $i$;
(3) $a_{i+a_i}$ is divisible by $a_i$ for any $i$.
For which positive integers $n \gt 1$ is this possible only if the numbers $a_0, a_1, \dots$ are all equal?
(1) $a_i = a_{i+n}$ for any $i$;
(2) $a_i$ is not divisible by $n$ for any $i$;
(3) $a_{i+a_i}$ is divisible by $a_i$ for any $i$.
For which positive integers $n \gt 1$ is this possible only if the numbers $a_0, a_1, \dots$ are all equal?