# Brilliant Math Contest

Algebra Level 5

To celebrate the new year, the Brilliant society decided to host a math contest. The results were fantastic, and Brilliant decided to award the top $$n$$ students with a medal $$(n>1)$$. For the first round, Brilliant awarded it to the top student, along with $${1}/{7}$$ of the remaining students (i.e. $$n-1$$ of them).
For the second round, Brilliant awarded it to the remaining top two students, along with $$1/7$$ of the remaining students.
This process continued, until the $$k^{th}$$ award, which was awarded to the remaining top $$k$$ students. However, at this point in time, there were no more medals left.

How many students won a medal? (a.k.a. what is the value of $$n$$?)

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