International Mathematical Olympiad 1967 Problem 6

In a sports contest, there were $m$ medals awarded on $n$ successive days ($n > 1$). On the first day, one medal and $1/7$ of the remaining $m - 1$ medals were awarded. On the second day, two medals and $1/7$ of the now remaining medals were awarded; and so on. On the $n$-th and last day, the remaining $n$ medals were awarded. How many days did the contest last, and how many medals were awarded altogether?