SILK-ROAD 2002 Problem 2

I tried to search SRMC problems,but i didn't find them(I found only SRMC 2006).Maybe someone know where on this site i could find SRMC problems?I have all SRMC problems,if someone want i could post them, :wink: Here is one of them,this is one nice inequality from first SRMC: Let $n$ be an integer with $n>2$ and $a_{1},a_{2},\dots,a_{n}\in R^{+}$ .Given any positive integers $t,k,p$ with $1<t<n$ ,set $m=k+p$ ,prove the following inequalities: a) $\frac{a_{1}^{p}}{a_{2}^{k}+a_{3}^{k}+\dots+a_{t}^{k}}+\frac{a_{2}^{p}}{a_{3}^{k}+a_{4}^{k}+\dots+a_{t+1}^{k}}+\dots+\frac{a_{n-1}^{p}}{a_{n}^{k}+a_{1}^{k}+\dots+a_{t-2}^{k}}+\frac{a_{n}^{p}}{a_{1}^{k}+a_{2}^{k}+\dots+a_{t-1}^{k}}\geq\frac{(a_{1}^{p}+a_{2}^{p}\dots+a_{n}^{p})^{2}}{(t-1) ( a_{1}^{m}+a_{2}^{m}+\dots+a_{n}^{m})}$ b) $\frac{a_{2}^{k}+a_{3}^{k}\dots+a_{t}^{k}}{a_{1}^{p}}+\frac{a_{3}^{k}+a_{4}^{k}\dots+a_{t+1}^{k}}{a_{2}^{p}}+\dots+\frac{a_{1}^{k}+a_{2}^{k}\dots+a_{t-1}^{k}}{a_{n}^{p}}\geq\frac{(t-1)(a_{1}^{k}+a_{2}^{k}\dots+a_{n}^{k})^{2}}{( a_{1}^{m}+a_{2}^{m}+\dots+a_{n}^{m})}$ :wink: