Question 120
In a mathematical competition, gold medals are given to $\lfloor \frac{n}{a} \rfloor$ people, silver medals to $\lfloor \frac{n}{b} \rfloor$ and bronze medals to $\lfloor \frac{n}{c} \rfloor$ ($a \ge b \ge c$ are integer constants and $n$ is the number of participants). No one gets two or more medals. Determine all triplets $(a, b, c)$ with the following property.
Property: For every integer $k \ge 3$, there are exactly two values of $n$ such that the number of people without medals is $k$.
* $\lfloor r \rfloor$ (written $[r]$ in the original) is the greatest integer that does not exceed $r$.
Property: For every integer $k \ge 3$, there are exactly two values of $n$ such that the number of people without medals is $k$.
* $\lfloor r \rfloor$ (written $[r]$ in the original) is the greatest integer that does not exceed $r$.