MathLabs

Problem 6

In a sports contest, mm medals were awarded on nn successive days (n>1n>1). On the first day, one medal and 17\frac17 of the remaining m−1m-1 medals were awarded. On the second day, two medals and 17\frac17 of the then remaining medals were awarded, and so on. On the nn-th and last day, the remaining nn medals were awarded. Find mm and nn.
Step 5 of 6: Apply integrality
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6n−1∣(n−6)6^{n-1}\mid(n-6)
Detailed analysis

Since mm is an integer and 6,76,7 are coprime, the formula forces 6n−16^{n-1} to divide n−6n-6.