Question 35
$n \gt 3$ positive integers are written in a circle. The sum of the two neighbours of each number divided by the number is an integer. Show that the sum of those integers is at least $2n$ and less than $3n$. For example, if the numbers were $3$, $7$, $11$, $15$, $4$, $1$, $2$ (with $2$ also adjacent to $3$), then the sum would be $14 / 7 + 22 / 11 + 15 / 15 + 16 / 4 + 6 / 1 + 4 / 2 + 9 / 3 = 20$ and $14 \leq 20 \lt 21$.