7. Solve the equation in natural numbers $2 n-\frac{1}{n^{5}}=3-\frac{2}{n}$

ANSWER: $n=1$.
Solution: $2 n=3-\frac{2}{n}+\frac{1}{n^{5}} \leq 3$, only $\mathrm{n}=1$ fits

Lomonosov Moscow State University

## School Olympiad "Conquer Sparrow Hills" in Mathematics

Final Stage Tasks for the 2015/2016 Academic Year for 9th Grade