Syler wrote: Let $ a_{1},a_{2},...,a_{n} $ be real positive numbers and $ k>m, k,m $ natural numbers. Prove that $(n-1)(a_{1}^m +a_{2}^m+...+a_{n}^m)\leq\frac{a_{2}^k+a_{3}^k+...+a_{n}^k}{a_{1}^{k-m}}+\frac{a_{1}^k+a_{3}^k+...+a_{n}^k}{a_2^{k-m}}+...+\frac{a_{1}^k+a_{2}^k+...+a_{n-1}^k}{a_{n}^{k-m}} $ We can write the ineuanlity as: $n(a_{1}^m +a_{2}^m+...+a_{n}^m)\leq\frac{\sum_{i=1}^{n}a_{i}^k}{a_{1}^{k-m}}+\frac{\sum_{i=1}^{n}a_{i}^k}{a_2^{k-m}}+...+\frac{\sum_{i=1}^{n}a_{i}^k}{a_{n}^{k-m}}=(\sum_{i=1}^{n}a_{i}^k)(\sum_{i=1}^{n}\frac{1}{a_{i}^{k-m}})$ And Chebyshev inequality will be useful~~~