Problem

Source: MEMO 2008, Single, Problem 1

Tags: inequalities, algebra unsolved, algebra



Let $ (a_n)^{\infty}_{n=1}$ be a sequence of integers with $ a_{n} < a_{n+1}, \quad \forall n \geq 1.$ For all quadruple $ (i,j,k,l)$ of indices such that $ 1 \leq i < j \leq k < l$ and $ i + l = j + k$ we have the inequality $ a_{i} + a_{l} > a_{j} + a_{k}.$ Determine the least possible value of $ a_{2008}.$